In Vilnius if you can get in I recommend Domus Maria. Modest charges, but a wonderful former monastery in old town right next to the Gates of Dawn. Secure parking in gated courtyard surrounded by high buildings. All sights within walking distance.
A bit austere - dining room more like a refectory. Only lunch served on site (apart from breakfast of course) but no shortage of places to eat a few steps away. Not unlike staying in a smart boarding school, and used quite a lot for conferences etc.. Can be hard to locate, but from the marketplace, go uphill keeping left towards Gates of Dawn and just past Russian Church and gift shop the entrance is on the left in front of the big church you've almost collided with ! If you want on site bar, spa, all the frills and room service etc, however, look elsewhere.
I stayed there early June this year.