Where should we live in London?

Us:  A married couple without kids.  One chihuahua going through quarantine requirements before the move.
Financially comfortable, in our mid-40's.  Moving to London for two years.

What: Want to rent a two bedroom place, convenient to public transportation.  Husband working in Uxbridge and may drive out to UB (or will take public transport) Wife has no desire to drive in London whatsoever.    

Wants convenient shopping and restaurants within walking distance.  Everyone and their brother is making plans to visit us, so easily getting into the city on the tube is desirable.
Where would you recommend we live in London?  TIA for your help

Uxbridge is served by the Metropolitan and Picadilly lines so towns along those make the most sense to start your search. How long of a commute is desirable?

I live in Ealing which I am happy to recommend. Chiswick, Kew and Richmond are also nice, although Richmond would be more difficult for a commute.

The metropolitan line has a stop at Finchley Road, which I don't know much about, but might be worth looking into as I have heard good things about Finchley as well.

Finchley Rd tube isn't in Finchley, just to be confusing, it's in West Hampstead, but still a pretty good area.

My husband ideally would want no more than a 45 minute commute one way.

I can second West Hampstead  (Hampstead if you can afford it).  The Finchley Road station offers an easy to get to Uxbridge using public transport and it is just a few stops from Central London in the other direction.  That said - driving during rush hour could be a pain.  I imagine it would be an hour or so each way, possibly more as the google map directions suggest using the North Circular road, which is notorious for horrible traffic.

Assuming traffic isn't a deterrent for your husband, the area offers loads of restaurants and shops.  Hampstead has a bit of history and even a few small museums. 

The Waterloo area is central to almost everything ie buses underground trains. But can be expensive to live schools good in that area also if you have children.

It's also a long way from waterloo to Uxbridge. For a 45 minute commute I'd look in areas at the top of the Metropolitan line or with links to it. Amersham is pretty nice.

To check out the quality of schools in a particular area, you need to look at the Ofsted reports:http://www.ofsted.gov.uk/