I'm assuming you want this to be a happy trip, and since it has to be cheap, pack light, pack light, pack light!
Here's what I would pack for a happy, inexpensive month:
2 pairs of capris or jeans
1 skirt (if you and your sister are church goers on a regular basis or if you intend to enter any of the famous churches, this will be 100% necessary, especially in Italy, where womens' fashions are more conservative, but you can leave it out if you intend to enter no churches)
1 bathing suit (can be left out if you don't intend to go swimming)
2 t-shirts
1 nice blouse (again, can be left out if no churches are in the itenerary)
1 extra pair of shoes
3 pairs of socks
3 pairs of underwear
1 extra bra
1 copy of all prescriptions
1 month's supply of any prescription medications
1 extra pair of contacts/glasses if you use them
Miscilaneous items that you might want to take with you would include a travel clothes line, half a tennis ball (for stopping up bathroom sinks to wash clothes), no-rinse body wash/shampoo caps (usually available at your local medical supply store), a travel journal, pictures of your home town and a map showing its location (to make friends with the locals!), and a list of contacts. You should also keep copies of your passport photo page and all other important documents in a location on your body separate from the actual documents.
Does this $5,000 include your passport? If you don't already have it, you'll spend ~$150 on it. (I'm assuming you and your sister are both over 16.)
Make sure that you have an up-to-date travel guide. Rick Steve's books are perfect for shoe-string travelers because that's what he specializes in. Frommer's is also excellent, but a dryer read and focuses more on the high-price accomidations.
Make sure you have a free e-mail address set up, such as gmail or yahoo, that you can check anywhere and use to keep in touch with family and friends back home.
Don't be surprised if, at a hotel, especially in southern Europe, the clerk asks for your passport. They have to register you with the police and use the nighttime hours to log all visitors at once. If you are uncomfortable with your passport being in the top drawer overnight, ask if you might pick it up later in the evening before you go to bed. They're usually pretty good about accomidating such a request.
I must disagree with greek gal on something. The Tube in London is NOT more expensive than the busses. Rather, you can get an Oyster card or a travel pass. Get one for zones 1-6. If you're only going to be in London for 2-3 days, just buy one daily. It's actually rather cheap to do it that way, and they're good on the buses, the trains within those zones (as far out as Hampton Court Palace), and on the underground, all without paying an extra pence. Definitely print out a travel zone map of London for this part of your journey.
Check out some of the free sights. I don't know about the rest, but in London, this would include the British Museum, the Victoria and Albert Museum, and Hyde Park. Some of the others, such as the Theater Museum, have one free day per month.
Overnight trains and sleeping skills can really help you and your sister to sleep for free. (Rick Steves' Europe Through the Back Door gives some amusing suggestions for this.)
To save money on food, picnic! It's easy to go into any supermarket and pick out fresh fruit, bread, etc. Or, go into a department store and follow the house wives until you see the salad bar. In Europe, they charge by the plate size, so get the small plate and pile it high to fill up for a smaller amount of money. If nothing else, McDonalds locations are plentiful.
You can find airfare a little cheaper, possibly. Have you made use of sites like Kayak? I found one flight for less than $600/person from St. Louis to London. Flights this cheap are easy to find if you're willing to fly on a non-refundable ticket and be one of the first ones bumped in case of over-booking.
Plan your itenerary carefully. Talk it over with your sister as to which sites you feel that you absolutely MUST see, which ones you'd really like to see but will cut out of the itenerary if you must, and which ones you feel would be nice, but you could take or leave.
Be aware of scams, such as "found" rings, friendship bracelets, other "tourists" asking you for directions, etc. Definitely check out the Graffiti Wall on ricksteves.com for the latest on various scams, cheap travel techniques, and even where to find the best chocolate.
Finally, be aware of what you can and can't take in your carry on. Nothing sharp. You can have 3 bottles, each containing no more than 3 oz of liquid, and all must be kept in a single zip-loc bag. If you choose to lock your carry-on, make sure that you use a TSA approved lock. Check the TSA website for additional information.
I really doubt you'll be able to make it for a month in so many places with so little money, but I do wish you luck.
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