A single word for 'regularly visited place'
Haunt seems a good synonym for what you seek, which according to Webster's is:
- "a place that you go to often."
Hangout is a common word for this these days:
a place where a person frequently visits, esp. for socializing or recreation.
A frequently visited place (TFD)
It can carry the meaning of favorite as well, but not necessarily (note that "favorite" is added as an adjective in the example):
a favorite place for spending time; also : a place frequented for entertainment or for socializing
The park was their favorite hangout. (MW)