I get PM's from time to time and I don't mind helping at all, but I think it better to do posts when possible. So this is in response to a PM
Thanks for all of your help and advice. We ended up booking a small/medium sized hotel in an area in the inner part of Budapest for a price, location, breakfast, wifi, and air condition that the 4 of us can live with. It is the The Three Corners Hotel Art, a little Belgium chain. We will be arriving by train from Vienna and have loosely organized our few days in Budapest like this:
Day 1 Afternoon of arrival day, walking tour of some Pest sites and dinner
Maybe walk up Vaci utca and then walk up to Deak Ferenc ter and take the 47/49 Tram back to your hotel Stopping at the Dohany utca Synagogue ("GREAT Synagogue") along the way (get off at the first stop and walk back a block).
Day 2 Great Market, Buda side sites, river promenade and evening Danube cruise
The Market is just a few minutes walk from your hotel or you can take the 47/49 Tram from Kalvin ter one stop to the Market. Then walk towards the river and look for stair going down. Go down the stairs and you will find the No.2 Tram Stop. Get on going left to right. This will take you to the Danube Promenade. Get off where ever you want and walk a bit of it. The Ambassador Café has excellent stuffed cabbage and great views (look for the orange awnings). Get back on the No. 2 and it will take you to the Parliament Building. Walk past the Parliament Building up Falk Miska utca which is the big antique street in town. Look for PINTAR which has the most interesting maze of connecting basements full of antiques. Continue down Falk Miska until you reach a major boulevard with a tram. Turn left towards the river and you will see the terminus of the No. 2 line one block down. The No. 2 will take you home.
Day 3 Churches, Andrassay, Opera area, Museum of Terror
Back on the 47/49 Tram to the Astoria stop (1 stop). Get off and continue walking to the second street on the right. Turn right on Dobb utca and then left on Rumbach utca and see the Rumbach Synagogue. From the synagogue continue on to the pedestrian route on your right. This will take you into the Gozsdu Courtyard which is interesting. Turn left as you walk through the courtyard area and you will come out on Kiraly utca. Turn right the first street on your left and that street will take you to Andrassy ut. (get a map for all of this, but it really isn't hard when you see it on a map). I would walk to the Opera and the House of Terror and then get on the metro nearly in front of the House of Terror, get off at the next stop and then get back on for one stop, then get off at Hero's Square. It shortens a very long --- but fascinating --- road that way.
Now you want to get back on the M1 Metro and ride it back to the Bajcsy-Zsilinszky stop. When you come up you will see the Basilica on your right. See the Basilica and then walk straight towards the river. At the end and on the right you will see the No. 2 Tram which will take you back towards your Hotel.
Day 4 check out and leave by early afternoon, catch up to something we didn't get accomplished on days 1-3 or ?
Go to Castle Hill in Buda. Take the No.2 to the Chain Bridge, cross on foot and take the Funicular up. 3 hours in Buda is generally enough to cover it if you don't do the museums. Then off you go....................