The tube station from Paddington goes everywhere! Well, everywhere in London. What sort of things do you like?
London has everything. The museums and art galleries are free as are the parks. You can walk to Hyde Park from Paddington in about 10 minutes or less.
If you like just sitting and people watching (I do) Covent Garden is a good place for that - all sorts get there 
Don't be afraid of the underground, it all connects up so if you get on the wrong one or the wrong way round, you can soon get back to where you're supposed to be, look on it as an adventure. I like to watch people and guess who are the commuters and who are the tourists (doesn't take much expertise in the power of observation for most of them). Then I give people names, occupations and destinations, the wackier the better 