A post from 2020 asking a similar question: https://community.ricksteves.com/travel-forum/slovenia/parking-and-accommodations-in-ljubljana
I stayed at the City Hotel in 2019 without a car. I liked it. It definitely is NOT a small, family-owned Rick Steves kind of place. It's more commercial hotel and had a very busy breakfast area.
I also considered Slamič B&B, listed in the former RS Eastern Europe now RS Central Europe guide. The RS guide notes free parking, and multiple reviews on the Booking website mention the convenience of parking while still being within walking distance to the Old Town. It appears it now markets itself more as a hotel. It also seems a little more costly than I remember it being.
https://slamic.si/en/
https://www.booking.com/hotel/si/bbslamic.html