An idea about travel, check as many web sites for airline routes as possible. If there are several different airports within 100 miles of your home try the air portion using different airport departures. Same with destinations and hotels. If you have the time and like to relax, look at positioning cruse (Europe to US in fall or vice versa in spring) This is when a ship is moved from say the Caribbean in winter to Europe in summer. The rooms are almost always really inexpensive and it can prove to be an economical way to get there. One warning, the ship has you hostage for that length of time, so you can possibly run up a large shipboard tab (drinks, specialty restaurants, shows...).
I agree with other comments about meals in hotels, you can usually find small establishments near by with excellent food for a lot less. Another idea for sight seeing is to see if the city operated a circle tour (jump on jump off) with set bus stops and a bus running every so often. These are susally inexpensive and a good way to see a city.