Hey there, and welcome!
Far as public RP goes, your best bet for walkup RP is the Withered Tree in Riften, which has a mixed reputation. It can be really good, but it can also be REALLY BAD. If you want something other than tavern RP, though, your best bet is to check the events calendar, on the top of this page!
Further, do you have any favorite races, or niches you're looking for? Maybe you have a mage, or a warrior? Maybe you love the fearsome Nords, or the sly Khajiit, or the.... interesting.... Argonians? Don't be afraid to tell us ideas for characters you have, it really helps narrow down the search for something that fits you JUST right.
Though, if you don't know for sure where to start, hub guilds are your best bet. They'll help you make connections, and get in touch with other people in the community. If you don't have Discord, yet, I also recommend you get it, as it is a must-have for OOC comms and coordination.
Happy to have ya! And hope to see you in RP sometime!
Feel free to reach out; I'm happy to RP, chat, PvE or whatever. (:
Want a dog for your character?