Does the hotel loan or rent basic bikes? If not, is there a rental place within a mile or so?
We have 4 bikes that guests can use if available. Yes there is also rental places within one mile.
I believe there are a few bikes near the pool - probably free to use. I would call them and ask.
I did not see any bikes for rent at the hotel. I would guess that are places nearby since the hotel is close to downtown. The best way to find out would be from the hotel itself or the Palm Springs Chamber of Commerce.
Get an answer from Villa Royale Inn staff and past guests.