Question for people who know about York & surrounding area

[AlexaShutUp]

Teenage dd and I will be spending a few days in York next week, staying near the city centre. I have a few questions and am hoping that someone who knows the area can help!

1. Apart from the Minster, what are the absolute must-visit places in the city? We quite like just mooching around and don't have loads of time, so don't want to go into full-on sightseeing mode, but don't want to miss anything really good either!

1. We'd really like to spend a day outside the city walking in the dales. There are package day trips that offer this, but I am wondering if we can just hop on a bus/train to somewhere instead. Are there any nice spots for walking that would be easily reachable via public transport?

1. Is there anywhere that you would recommend in the city centre for a nice afternoon tea one day?

Any other suggestions more than welcome! TIA!

Lots of really helpful info, thank you so much to everyone who has commented. I'm really looking forward to our trip!

Agree that Betty's is massively overrated and over priced. But the fat rascals are lovely

The Dales and moors are different areas, both look different and stuff as well. The moors are nearer to York, you can get the (regular) bus from there to Whitby and theres the steam train through the moors at pickering.

I think Scarborough is a bit bleak these days, Filey and Whitby are nicer I think. I like Dalby forest aswell

Don't forget Barley Hall off Swinegate , well worth a visit.

We actually quite enjoyed yorvik and booked in advance so we didn't have to queue - and the queue is usually extremely long ! Also there is a place called Dig which is a kind of archeology museum/experience - maybe for younger children though. Heard good reviews of the Chocolate museum but not been.
Definitely walk the walls - it's interesting looking down into the houses along the way and brilliant views of the minster.