All around the kingdoms are stables where one can leave their mount in
relative safety. Some stables charge a small fee for total safety. More
and more stables are starting to offer this service.
On a roleplay note, please make sure when you are using stables that service
a certain type of customer that it is in character to do so. For instance a
stables in a temple, is technically set up just to serve those of the faith.
A rogue for instance would not house their mount in the Halls of Justice in
Waterdeep. Make sure you find an appropriate place to house your mount.