How do you say "favorite" in latin?

There are various possibilities depending on the required shade of meaning (in Latin, you must be very specific!):

• carissimus (dearest, the one most valued)
• dilectissimus (the most beloved)
• gratissimus (the one most liked or enjoyed, the most agreeable)
• iucundissimus (the one giving most pleasure)

and probably many others.

So e.g.: "Roma est mihi omnium locorum iucundissima" (meaning it is most pleasurable for you to be in Rome), or "Roma est mihi omnium locorum carissima" (of all places, Rome is dearest to you) etc., make your choice.

For the other sentence, I suggest:

• "Aliis omnibus quae mihi proposuisti animalibus felem praefero." ("From all the animals you have offered to me I prefer the cat.")

Or:

• "Omnium quae mihi proposuisti animalium gratissima mihi est feles." ("Of all the animals you have offered to me I best like the cat."