Will you come and visit me in hospital when I have my operation?
We don't use an article before certain nouns (places) when we talk about being at the place for its 'normal purpose'.
These include many everyday places, incuding
in hospital (British English; Americans say 'in the hospital')
at sea (Compare "on board" a ship, train, aircraft, etc)
at university (British English, but 'at the university' is also used in BrE, and is the norm for American English)
If you go to one of these places 'as a participant' you also leave out the article. But we don't *'go to home' in standard English. And 'go to town' also means, informallly, 'perform or do thoroughly, etc.'
I adapted a list found in Oxford guide to english grammar (1994, 2002) by John Eastwood. Regarding university the author writes:
(studying) at university, go to university (to study); But at/to the university is also possible and is normal in the USA.