Cracked rim around the spoke

Cracks in the wheel rim do generally need attention. If the cracks are around the nipple and you're a gambling man you can keep an eye on the crack's propagation and maybe use it a little, if they're in the side/wall, it's possible failure will be a little more exciting.

If you purchased them recently you may wish to return or exchange them.

Welding is probably not an option (assuming they're aluminium).

is it okay to ride

Yes, until the next bike shop or similar. Be careful you may have a catastrophic failure without notice (think about sudden falling in front of a truck), do it at your own risk.

or is it okay to weld them.

No, if done cheaply likely to be of low quality (then see above), if done properly as expensive as replacing them.

You can save some parts from your wheel (hub, cassette ... maybe even spokes) so a new wheel may be cheaper than you think. Get in touch with your local bike shop/cooperative

I found a couple cracks where the spoke sits around the back rim.

There are a number of reasons why rims develop cracks:

• The rim is so light weight that it's not even supposed to last. A quality 622mm rim will weigh over 500 grams.
• The rim may not have double eyelets. Almost always, these cracks are found on rims that are double wall rims but lack double eyelets to distribute the high spoke tension evenly to both walls of the rim. Thus the outer wall that is over-stressed cracks. To avoid this problem in the future, choose a rim that has double eyelets. Note double eyelets have compatibility issues with tubeless tires. Considering that tubeless might not be such a good idea after all, the choice between rims that don't crack around the spoke holes and tubeless is easy: choose the types of rims that don't crack.
• The rim may be anodized. Anodization is an optimal surface for cracks to appear and grow. To prevent this problem in the future, choose rims that have a high polish finish. The smooth surface of a polished rim is not a surface where cracks would easily appear. But oh, you can't buy polished rims anymore because everything has to be black nowadays. Fortunately, rim manufacturers have discovered that it's possible to make black rims by powder coating instead of anodizing. Powder coating doesn't have a tendency to crack. Choose a powder coated rim over an anodized rim.
• The rim may have too few spoke holes. Historically, quality wheels where made with 36 spokes. However, after The Great Spoke Scam, wheels with fewer than 36 spokes started to be fashionable. Resist the fashionable tendency to choose wheels with fewer spokes and choose wheels with full complement of spokes (36). Note the Sheldon Brown's advice about front wheels needing fewer spokes than rear wheels is obsolete today due to the prevalence of disc (hub) brakes. The advice to choose fewer spokes on the front wheel may have been good advice when rim brakes were used, but not so good advice anymore with disc brakes. 36 front and 36 rear is optimal.
• The spokes may be of an incorrect type. Ideally, spokes should be as thin as you can make them (so the elastic thin spokes distribute spoke tension over a larger number of spokes). However, spokes have a tendency to fail on the threads or J-bends so these sections should be made thicker. The ideal spoke used to be 1.8mm/1.6mm/1.8mm when the spoke holes in the hubs were made for 1.8mm spoke J-bends and threads. However, today spoke holes of most hubs are oversized to make spoke installation fast (which may result in less wheelbuilding minutes but definitely won't result in a good wheel), so spoke manufacturers have started to offer 2.34mm/1.8mm/2.0mm spokes which may be the optimal fit for today's hubs with ridiculously large spoke holes.

By following these advices (not too light rim, double eyelets, polished or powder coated rim, 36 spoke holes, 2.34mm/1.8mm/2.0mm spokes) you will get a strong wheel but the wheel needs to be properly built too: the builder must tension the spokes to an even and high tension, the builder must take spoke winding into account when tightening the spokes, and the builder must stress relieve the wheel. Wheelbuilding machines usually don't do these steps so machine-built wheels are not as strong as handbuilt wheels.

Fear not, there are cyclists weighing over 100kg riding on over 15kg bikes transporting 30kg cargo and properly built wheels don't fail for them in any manner.

So what can you reuse on your existing wheels?

• If the hub has 36 spoke holes, you can reuse it; otherwise it should be discarded
• If the spokes are triple butted (2.34mm/1.8mm/2.0mm), you can reuse them; otherwise it's better to start with fresh spokes
• If you can find a rim with at most few millimeters of difference from the effective rim diameter of your current rim, you can use the same spoke length (so reusing spokes is a possibility if they're good enough quality); otherwise you need a different spoke length
• Nipples could be reused but if you have the unfortunate experience of using aluminum nipples it's better to replace them with brass nipples. Also, recently nipple manufacturers have improved nipples with a spherical seat (for example sold as DT Swiss Pro Head nipples) as opposed to a conical seat, and nipples are cheap anyway so if your nipples don't have a spherical seat or they aren't made of brass, it's better to start with new good nipples.

Is it okay to ride or is it okay to weld them?

No, it's not okay to ride apart from making a short ride safely home and/or to the bike shop. The wheels will eventually fail catastrophically.

its a tight one at the moment, i haven't really got the money to be spending another £100 on just one wheel.

A new wheelbuild costs perhaps around that. To add the nipples, spokes and quality rim you are spending nearly double that. To add a new hub (if your existing hub doesn't have 36 spoke holes) you'll be spending way over double the stated £100 amount.

But of course there could be countries where labor is cheap. In such a country, if your existing hub has 36 spoke holes, you could theoretically be able to get a quality wheel for as little as £100. But do note there may be a reason for labor being cheap -- for example, a wheel built by a good wheelbuilder will last thousand times more than a wheel built by a bad wheelbuilder.

I would definitely not ride these; if a spoke were to suddenly rip loose, you could immediately find yourself with a very squirrely ride.

If you recently purchased these I would take them directly back to the shop where you bought them. No wheel that has not been actively mistreated should be coming apart in under a year.

I don't know what kind of warranty they might have come with (hopefully they have at least a few months'), but if you can get them back to the dealer fast enough they'll be the dealer's problem to resolve. Depending where you are, you may have anywhere from a week to a month to take things back and simply void the sale if they're not fit.

I had a wheel fail on a new bike after 3 months in a similar fashion, with the nipples tearing the rim apart; the shop took a look at it and had the manufacturer warranty the wheel. (The rim had a rectangular profile, and the flat plane that the spokes pulled against was tearing away from the braking tracks at the bend. On both sides and in multiple places around the rim.)

You can probably ride the wheels for a little while, but I would keep an eye on them and replace the rims as soon as possible. I believe the risks of catastrophic failure are relatively low*, because I've had a couple of wheels on which the spoke pulled part of the surrounding rim through, and I discovered them simply because the wheel started rubbing the brake. In essence, the effect was no more catastrophic than a single broken spoke. *I would not, however, go bombing down hills or similarly risky stunts until the wheels are in good shape again. You are looking at a short time frame (a month or two?) until the wheels are no longer rideable.

As others have said, if you bought these wheels new, take them back to the shop and ask for them to be made right -- either new rims or replacement wheels. Wheels that aren't abused should last for thousands of miles.

Hubs can almost definitely be reused. Steel spokes can be reused if they are the right size and aren't corroded. Good luck!