Hotels are expensive in the UK. $200 is probably average. When I stay in the UK I stay in the budget brand Premier Inn. It's basic and seriously non 4 star, but it's clean and convenient. I'm only going to be putting my head down for the night after all.
I just got back from the West Country. Beautiful!!!
Nowhere in the UK is particularly great in late Autumn/Winter, unless you are after moody grey skies, frost, wind and rain.
Bath is incredible. Stonehenge has to be seen, but is a little diminished by restrictions compared to a decade or so ago.
Places like Salisbury and Winchester are steeped in history. It's been a while since I visited those town centres and Cathedrals, so I will defer to John above.