Country Inn & Suites By Carlson, New York City in Queens, NY. Does this work? $85 a night inc. breakfast, wifi etc for a queen room.
Aw drat. As you can imagine it’s pretty popular.
I clicked the link but it just gave me the generic search form. That’s a low-end but reputable chain. The thing I would want to know is the exact location of the hotel. Most of the inexpensive hotels are near JFK, which is… extremely far from Manhattan. Also on Tripadvisor.com you can read reviews for the particular hotel, if you didn’t know that already.
National Museum of the American Indian - on the southern tip of Manhattan near Wall street. This is actually a Smithsonian museum, so it’s free. It’s also just a short walk to the Staten Island Ferry (A must-do for its close pass of the Statue of Liberty - plus… free!)
The Tenement Museum chronicles New York immigration of the late 1800s, while the Merchant’s House is a window into middle-upper class life in the same era.
The New York Transit Museum has a variety of exhibits about the iconic transportation system, including entire retired train cars with period ads and all manner of subway paraphrenalia. If you were to stay in Brooklyn Heights, it would be walking distance from there.
Forbidden Planet is a SF/comics bookstore with a large manga section.
OK, somehow the link worked just now. It’s a couple of blocks from the 21st St.-Queensbridge station on the F-line or Queensboro Plaza on the 7. A short ride into midtown Manhattan. It’s not the greatest neighborhood. Not dangerous, really, just a bit run down and industrial. (Try Google street view on the address, you’ll see what I mean). So if you’re not dead set on staying in some charming, adorable neighborhood, its in a good location if you’re satisfied about the reviews you read.
ETA: I don’t want you to think it is a neighborhood on the skids - it’s the opposite, LIC is rapidly hipsterizing.
Beware of bedbugs if you are looking at cheap NYC hotel rooms – take precautions so no little friends go home with you. (They can also infest not-so-cheap hotel rooms.) I was going to suggest the Greenpoint YMCA where I stayed some years ago, but I see lots of people complaining about bugs there…
Run!!!
Er, I mean, welcome, welcome! 
Would she be interested in Liberty Science Center? It’s an interactive science museum that’s pretty accessible from Manhattan. I was there once years ago, and it was pretty fun.
What are *you *worried about? He’s invading your downstairs neighbours, not you! 
[Also, just beware of bedbugs in general. They seem to be everywhere these days. Lots of stories about services “discretely” cleaning high-end hotels and offices and the like. They’re not respecters of class or boundaries.]
The Country Inn is a mid-scale (but on the nicer side) chain of hotels - I stay there often enough to be a member of their rewards program. I have not stayed at that particular motel, however.
I highly recommend the Rose Center for Earth and Space. http://www.amnh.org/rose/visitorsguide.html
Tripadvisor! I hadn’t actually thought of that. :smack: That hotel I was looking at in New York has good reviews, including comments about no bed-bugs, so I think I might as well go with it. Hunting out hotels in DC now. One of them says it has ‘dial-up internet.’ 
@Hello Again and Bogette: those are exactly the sorts of places that would interest us both; I’ll do what people on these threads usually do and print it out to take with me. Although we will have computers and wifi access and won’t be out that late at night, so I’ll probably be coming on the Dope even while on holiday.
While you’re down checking out NMAI, and the Ferry, get lunch at Sophie’s, a very fast, somewhat loud, deliciously tasty Cuban restaurant located at 73 New Street - a nondescript street that parallels Broadway. You can see investment bankers and government lawyers in their native environment 
At Trinity Church, you can view the grave of Founding Father Alexander Hamilton (it discretely says nothing of the fact he died in a duel) and contemplate the fact that in 1880, Trinity was the tallest building in Manhattan.
I gave you the wrong link for Forbidden Planet. It’s here:
Helpful websites:
hopstop.com - combines directions for public transit with turn-by-turn walking directions
On google maps, search New York, NY or any specific address. Touch the “Satellite” box to see more options, and select “Transit” from the popdown. You will see the subway lines overlayed on the actual geographical maps of NYC. The standard subway map is not to scale and can be misleading.
BTW, you can get a standard subway map free from any kiosk, and you should not rely on any subway map published in a guidebook that is more than 1 year old.
I travel to DC a lot, and always use Priceline.com for reservations. You can bid on a 4* hotel for $90 in Dupont Circle (great neighborhood) and you’ll almost always get either the Omni Shoreham (great hotel, a half block to the Metro and a couple of blocks to the National Zoo, of the Washington Hilton. The Hilton is a few blocks to the Metro, but closer to the actual Dupont Circle. The rack rates at these places are around $300/night.
They both charge for in-room internet access, but it might be free in the lobby.
Too late - I’ve booked our hotels now. Thanks anyway.
We decided to go with that Queens hotel after looking at loads of others (and checking on the bedbug reporting site), and we’re at the Washington Plaza, which looks central enough and has lovely big rooms and a pool. I was surprised at the price there - in dollars it’s about $161 per night, but that’s for two double beds, breakfast and free wifi (and all taxes).
All I have left to book is the Amtrak tickets. I take it it’s not really worth getting a New York Pass? We’re planning on visiting mostly museums, like the ones recommended in this thread, rather than the costlier places. (And there aren’t available tickets to go into the Statue of Liberty when we’re there, boo).
That’s a great neighborhood in DC–not too touristy. If you’re a beer aficionado and want to have a nice meal out, head to Birch & Barley a couple blocks north of the hotel.
Looks like you’ve got a good bit of quality advice here, so I’m going to pluck the low-hanging fruit:
Today!
After an awesome time in LA, we’re now in NY, and exhausted. If anyone’s around over the next few days (we’re leaving Monday to go to Washington) and wants to meet up, that’d be great; post, message me or g+ me. I should have started a thread or something, but I just haven’t had the time.
Glad you’re having a great time! How long will you be in DC?
nvm
3 nights/4ish days. Arrive Monday, leave Thursday.
We also went down to San Diego, but only to Seaworld.
This threw me for a moment, until I realized that NMAI actually has two locations, one in Washington (alongside almost all the other Smithsonian museums), and the one in New York.