Yeah, that's a good option; you can get the Picadilly line down from Russell Square to Hyde Park Corner in no time and then you're right on the edge of the park. From there you have the choice of Hyde Park, Green Park, St James' Park, all of which are nice and traffic free. I'm sure some people will chime in with some nice routes around there in a bit!
Otherwise you can hop on the city's hire bikes, to get down there, they're great for getting around, but you kind of need to know where you're going!
If you just want a quick session though Regents Park is great too though and if you run up to Euston Road and then westward to the park it should be easy enough to be able to run there and back rather than getting on the tube.
If you're there on a Saturday morning you should totally head along to one of the parkruns too (see parkrun.org.uk
) they're a completely free, timed 5k in loads of parks around the city, every Saturday at 09:00 am. You can register online if you want your official time but if you're not fussed just can just show up. They're usually a great atmosphere with all levels of people going along, from top club runners racing it in the 16s to old folk power-walking it round in 30+ mins.
Edit: fixed link