The Serpentine Running Club's website is an excellent resource.

It's about four miles around Hyde Park. If you add in a loop around the Serpentine itself, you get another two miles. Hyde Park's a very easy place to run, mainly because it's flat and traffic free.

However, it can get a bit dull because, at the end of the day it's just running in a park which looks more or less the same all around.

I would definitely recommend making it to the Heath - but try to do this during daylight hours, as it's a bit hard to navigate when dark out if you don't know it well (and December in London can be a LOT darker than in Arizona - take it from a native Tucsonan ). The view from Parliament Hill (southern end of the Heath) is IMHO the best in London; you can see almost everything for about fifteen miles in SW to SE-erly direction.

Of course, an alternative is running on the roads or along the river. I've been running in London for a few years (have done three marathons and a few halves) and actually, it's not all that bad, as long as you don't run through Zone 1 too much. I even run right up Whitechapel Road occasionally when I run to or from work.

Anyway, the London Marathon website has an excellent page whereby you can see all suggested routes in your area. Here's the link:

http://www.realbuzz.com/flmroutes/

You just click on the "Start Mapping Here" button to launch the app. Once inside, you don't have to create an account if you don't want. Anyone can see the routes.

I typed "Tower Bridge" into the "Jump to Location" bar, and it brought me to a spot just a bit south of Tower Bridge. You can drag the map up if you want. I also ticked off "Show routes on map", and it literally shows you every route which has been mapped by all London Marathon runners who are starting from your area.

It should be really straightforward, but please feel free to ask any questions.

Best of luck to you. ^