Hi, I live in York and you’ll have a great time, it’s a wonderful place. It’s very walkable, small and easy to navigate.
I wouldn’t bother with the bus tour as you have to go round the outside of most of the good bits of the city. I also wouldn’t bother with the GhostBusTour if you want history, it’s quite shouty and daft (which is fine if you just want a fun nonsense bit of entertainment). You don’t mention kids but the Wizarding Walk is very good if you do have them. Otherwise there are lots of walking tours you can join.
The Minster is fantastic, see if you can do a Tower tour as that’s interesting and you get good views (many stairs though ) and make sure you go into the Chapter House. Deans Gardens round the side is lovely and leads to some interesting streets.
Yes to Treasurers House (you might need to book a tour for that in advance, it’s national trust).
Cliffords Tower has been renovated recently and is now really excellent. Combine that with a walk along by the river and a trip to what was Dyls but is now Sophie’s - you can sit outside by the river or up in a little turret room for lovely drinks or lunch or cakes etc.
Shambles is iconic but crowded, but go out early for a walk (before 9am) around the centre of York and you’ll have lots of space for photos. The Shambles has got a lot of scaffolding up at the moment though.
Fossgate for cafes and some independent shops. Stonegate for more small shops and many jewellers. Low and High Petergate ditto.
Walk round the walls. Total loop is just under 3 miles but if you don’t have time for it all I’d get on at Layerthorpe and walk anti clockwise round to Bootham bar as you get the best views of the back of the Minster and other interesting stuff like lovely gardens. Stop off at Monkbar gate for gelato from Roberts. One of the bar gates on the walls holds another small historical museum.
Walk along the river - head down to Judi Dench Walk and along from there.
Jorvik is fun but short. Not sure I would bother if no kids unless you’re very into Vikings.
Dick Turpin’s grave is near Walmgate.
Bar Convent museum is good and you can reach that by walking up Micklegate which has interesting shops and cafes and Partisan and Skosh mentioned by another poster. Also off Micklegate are interesting streets to wander around if you like churches and quirky doorways etc.
The cat trail is a good way to see a lot of York on foot.
Museum Gardens is lovely and you can get to the Yorkshire Museum from there.
The art gallery is fine, they have a good ceramics room upstairs and a lovely outside space at the back and may be doing the summer pop up bar there again too.
personally I’m not a fan of Castle Museum but others love it. The Dickensian street there is good but everything else is a bit tired and it’s a bit of a mish mash of eras, in my opinion!
happy to help with any other pointers if useful.