For a day trip, you could hit Oxford and Warwick castle in the Cotswolds the same day. Both very cool places. I also love Bath and Stonehenge is cool to see(you don't need to spend more than maybe 30 minutes at Stonehenge).

For food, I keep hearing that England has great Indian food. I have yet to have great Indian food in England anywhere. I have had ok - good Indian food, but not great. I've had more authentic Indian food to what I've had in Delhi in SLC at a couple of different restaurants. My favorite places to eat are the pubs there in London. One of my favorites is Simpson's Tavern. It is frequented by the locals, including the current mission president in that area. Awesome food. Get the victorian pork chop...it is awesome.

I would do the London Pass. My two favorite places to go is the Tower of London and Westminster Abbey. I never thought the Crown Jewels would be all that cool, but the first time I saw them I was floored at how incredible they are. Every time I see them, I am in awe of them. And Westminster Abbey is incredible. I have ancestors that are buried in Westminster Abbey, so it's very cool to see their burial locations in the Abbey.