BibLaTeX: How can I remove the comma after "school" in @thesis entry?

The answer to Change the order of the pages and year in Biblatex, whose code you are using, uses quite blunt instruments to move the date printing after pages. This may not be exactly what you want or need in all situations.

Here is a slightly more complex setup that moves the date only if there are pages (or a chapter), which may result in an output that works slightly better for you in some situations.

documentclass{article}
usepackage[ngerman]{babel}
usepackage[backend=biber, style=numeric]{biblatex}

newtoggle{bbx:datesuppressed}

renewbibmacro*{date}{%
  ifboolexpr{
        test {iffieldundef{pages}}
    and test {iffieldundef{chapter}}}
    {printdate}
    {toggletrue{bbx:datesuppressed}}}

renewbibmacro{volume+number+eid}{%
  printfield{volume}%
  setunit{addcommaspace}%
  printfield{eid}}

renewbibmacro*{issue+date}{%
  toggletrue{bbx:datesuppressed}%
  iffieldundef{issue}
    {}
    {printtext[parens]{%
       printfield{issue}}}%
  newunit}

newbibmacro*{date:print}{%
  iftoggle{bbx:datesuppressed}
    {togglefalse{bbx:datesuppressed}%
     printdate}
    {}}

renewbibmacro*{chapter+pages}{%
  printfield{chapter}%
  setunit{bibpagespunct}%
  printfield{pages}%
  newunit
  usebibmacro{date:print}%
  newunit}

renewbibmacro*{note+pages}{%
  printfield{note}%
  setunit{bibpagespunct}%
  printfield{pages}%
  newunit
  usebibmacro{date:print}%
  newunit}

renewbibmacro{institution+location+date}{%
  printlist{location}%
  iflistundef{institution}
    {setunit*{space}}
    {setunit*{addcolonspace}}%
  printlist{institution}%
  setunit*{space}%
  usebibmacro{date}%
  newunit
}

begin{filecontents*}{jobname.bib}
@phdthesis{mythesis,
  author = {Me, I.},
  school = {University},
  title  = {Sometitle},
  year   = {123},
}  
end{filecontents*}
addbibresource{jobname.bib}
addbibresource{biblatex-examples.bib}

begin{document}
nocite{mythesis,sigfridsson,westfahl:space}
printbibliography
end{document}

As Alan explained in the comments under his answer, biblatex's punctuation handling is asynchronous: Punctuation is stored in a buffer and only printed once it is needed (i.e. when the next print... command actually prints something). Since in the code in the question the usebibmacro{date} in institution+location+date doesn't actually print the date, the setunit before it does not ultimately control the punctuation before the date. The date is only printed by date:print in chapter+pages, at which point other setunit commands will have added different punctuation into the buffer.

nopunct sets a permanent marker not to print any punctuation until new content/text is printed by a print... command. In this case it helps to suppress the undesired period. Since nopunct can be used inside and outside the punctuation tracker it is a handy tool to tweak punctuation, but I generally try to avoid it and prefer solutions not using it, as it can have effects that go beyond what is desired.