That's enough for one month, but not two assuming your airfare is not included in the $3500. Prices depend on exactly where you start from, where you fly into, the kind of places you stay and what you see/do/eat, how many people are going ... . People who backpack generally can get by for $100 US per day staying in cheap hostels and carefully watching their budget (not including airfare). However, if you stay in hotels, it will cost you more. I usually spend 100 to 150 euro a night for a hotel just for myself, but there are cheaper places.
Here are some resources that can help you plan and check options and current prices for your trip (expect prices in the future to rise):
http://www.kayak.com/ - airfares & hotels; the explore function is useful for finding the less expensive places to fly into from your starting point.
http://www.skyscanner.it/ - particularly good for budget flights within Europe, but you can also use everywhere as a destination to do something like the explore option on Kayak. You may not need the airfares, but you can compare to the cost of the trains to get around. this one may be more useful for you.
http://www.seat61.com/ - a great train site with details about railpasses. It can be cheaper to buy individual tickets than passes. This site will tell you how to determine whether you're better off with a railpass or individual tickets or some combination for your trip. It also details how to use the pass and what to avoid to get the best use out of a pass.
http://www.venere.com/ - hotels/B&Bs - prices for the same hotel can vary hugely depending on the season and what local events are going on.
http://www.hostelbookers.com/ - hostels.
http://www.monasterystays.com/ - monasteries & convents that offer accommodations
You can also look into camping or couch surfing as cheaper alternatives for accommodations.
http://www.backpackeurope.com/ - information & advice
For sightseeing prices: check the websites for entrance fees for the museums & galleries you're interested in. I spend anywhere between nothing and 40 euro a day depending on exactly what I go to see when out exploring. For food, I spend around 25 to 50 euro for a meal, but you can eat for less. A pizza is 8 to 13 euro and a panino or wrap is around 3 to 6.50 euro in many places. You can often get food at festivals at a relatively low price. You can also shop in the markets and put some meals together for yourselves.When I travel, I like to try the local specialties and the good restaurants.
Tough.
Assuming that excludes the airfare. If you stay in youth hostels, you can get away with 20...30 Euros/night including a simple breakfast/lunch/dinner. 60 days at 30 Euros are 1800 Euros, which will leave you with 1700 Euros for travelling, entrance fees, additional food etc. -> it'll depend on where, how and how far you want to travel - and what you want to see. Some attractions will gobble up that daily budget for a single entrance fee.
If you're not spoiled with food and accommodation, you can do it. Definitely research about couchsurfing, that will lower the costs tremendously. Buy breakfast and dinner in supermarkets (buns, ham, spread...) and eat lunch in normal local restaurants. Check which countries have potable tap water so you don't have to buy it. But avoid drinking it after heavy rainfall.
Maybe this site can also help you finding nice affordable hotels www.thehotelcompare.com they have great deals on hotels anywhere. Every time I travel I used this one and always find very good deals on hotel and I save some money too.
There are dirt cheap hotels but you will have to sacrafice luxury. Also fly with RyanAIr or EasyJet when you can. CHEAP CHEAP CHEAP. You can get a flight from the UK to New York for ￡15, which is like 25 dollars.
