April, eh?
I'm munching a ham roll as I type, so please excuse the crumbs.
April can be a mixed bag as far as the weather is concerned, so you'll just have to cross your fingers and bring a brolly for possible rain, a thick jumper just in case it's cold, and a thong bikini because it can sometimes be quite nice and warm.
I'll come back with more later, but for now I'll post these to get you started.....
First off, if the weather's OK, I would highly recommend a boat trip from Westminster (not far from your location) down to Greenwich. The link will give you most details, but I can say that it makes a bloody good day out, and is very interesting.
There are several firms that do these trips, but this one is about the best value (IMO).
Boat trips.......Westminster to Greenwich
http://www.riverthames.co.uk/boat/cruise/london/74.htm
Loads of info on this site.........
London Tourist Board (loads of stuff)
http://www.visitlondon.com/
And train details (for Paris)
Train to Paris.......(Departs from Waterloo)
http://www.seat61.com/France.htm#Eurostar
or.........
http://www.eurostar.com/UK/uk/leisure/travel_information.jsp
One little thing you should look out for, is a book called "The Guinness Superlative Guide to London."
It's probably out of print now (why oh why?) as it came out in the 80's(?) and they never carried on with it.
I read the entire book from cover to cover, and found it absolutely fascinating.
Done as a guide for tourists, it lists possibly two hundred locations which are off the beaten track, and most of them are amazing! I never knew that these little places of interest existed until I read that book.
It is brilliant for when you are going to a major tourist attraction, and pass by a little side road on the way that has one of these gems lurking in the shadow.
Personally, I find them far more interesting than the usual London tourist traps.
I'll see if I can find a used bookshop in the USA that has one in stock.
Oh, and go have a ride on the London Eye. If you're OK with heights, it's well worth it. Pick a clear day, and expect to queue for a short while.
Back later.