London for a week

Since it's your first time, I'd suggest the London Eye for sure. The panoramic views are fabulous and both of you would enjoy it. The tricky part is doing it on a day and time when you've got good sunshine and the lines aren't too long.

We also found Hampton Court to be a nice place to visit on a sunny day with all of the gardens and flowers in full bloom. It's only a 25 minute train ride from Waterloo station.

Things I enjoy doing : 

The markets. A particular favourite is Borough Market (upmarket food) on a Saturday lunchtime. Turn up, grab a coffee from Monmouth's, wander round, have some lunch from one of the stalls (chorizo from Brindisa, raclette from Neal's Yard, burger from the Ginger Pig or a pie from Pieminister, for example).

The Thames. The South Bank between Tower and Westminster Bridges is a great place just to wander. There's quite often events on around Butler's Wharf on a weekend, too. There's loads of attractions on the way, too, and the espresso bar in the Tate modern is great fun.
 

River Boats. There's tour boats, but that's not something I tend to enjoy. But there's also a number of commuter services sprung up along the river detailed here. The Greenwich-Savoy section is particularly fun, and the Richmond-Hampton Court is easily the prettiest way to reach the palace!

The science museum is cool. So is the London Dungeon.  Madame Tudsauds wax museum was awesome!!!