How long are you planning on being there? If you travel cheaply you can probably get by on US $100/day (not counting travel to and from Europe) though if you plan on drinking a lot, prefer not to stay in hostels and are thinking of having a LOT of fun in Amsterdam then you may need to spend a lot more. Also you probably won't say any money by taking trains to outlying cities rather than a main city.
The Best Book for Backpackers to Europe is the "LET'S GO" much better then Lonely Planet more up to date as well. Buy a Euro-rail Pass it will save you some money on trains yet they are valid for a certain amount of time. The distances aren't far in Western Europe so intercity travel shouldn't take up most of your leisure. You could ''couch surf'' or join Hospitality Club or look up what you want to do, where to stay then take it from there. Rock bottom one could get by on $25.00 per day if they couch surf then did walking tours with a guide book. It would be meals & entrance fees that would add up yet a lot of Europe could be visited without entrance fees.
Keep the important money/passport/ID down you pant, have a fake wallet with a few bills as a decoy so you don't loose everything. Southern part of Europe can get a bit rough in area. Take a debit/credit card, so the can be replaced, instead of money. Travel Light.
It's easy to work out what to see and do in a city. But Belgium is a whole country. You have to know in advance why you are going, what you want to see, and where those things are (or you will waste a lot of time trravelling).
What's special in Belgium (please note I haven't seen all of Belgium, this is just places I've been to)
First World War memorials and battlefields (deeply emotional)
Crusader castle at Bouillon
Waterloo battle site where Napoleon was finally defeated
Bierodrome (a bar in Brussels that has at least 400 beers)
La Morte Subite (a bar in Brussels that captures the First World War atmosphere)
just take a backpack
If you have decided to explore more than one points then you must be aware of attractions those you exactly want to explore. Europe offers plenty of such fabulous places where a backpacker could have a best adventures journey. But Where ever you are going to just pack lightly. If you don't..! so even you can't enjoy yourself with heaver luggage. I would also suggest you to don't miss to visit enhancing charm of local attractions as well. During my Paris tour i did great fun their and did skating along the road i simply had joyed myself. I will suggest you to must enjoy yourself and be safe feel free......Best of luck
Traveler cheques are better than carrying cash. Come clothes.
I meant berlin not Belgium
You named two cities and a country, though.
keep safe and fin trip!
