More and more, budget airlines like Ryanair, Vueling, and easyJet are a viable, relatively low-cost way to get around Europe, but rates can vary depending on the time of day and day of the week, and they can come with strict baggage policies, so you have to do some research to compare prices and convenience. You also have to factor in getting to/from the airport, extra time for checking in, getting thru security, etc.
As for researching restaurants, if you're really concerned about eating for the minimum cost, bring some Ziploc bags with you, and get meat, cheese, olives, bread, etc. at supermarkets, then use those ingredients for sandwiches. Eating local dishes and ingredients has always been a big part of our trips, especially for France and Spain, so keep an eye out for street markets, or restaurants with the equivalent of a "blue plate special" or prix fixe menu that will allow you to eat well for a decent price. Bring a water bottle and fill it up at every opportunity - bottled water, IMHO, is pricey! Learn the local term for tap water, and request that at restaurants and cafes.
Some museums offer free days and/or nights. The Prado in Madrid, arguably the best art museum in the world, is free in the evening. With several nights in Madrid, you could go there for an hour or two on several nights. Of course, you might find places busier then, accompanied by other bargain seekers. Are you a student, or can you qualify for other discounts? Some cities offer a discount pass or card, saving you on admission fees to sights and/or transportation around town - Rick Steves' guidebooks will tell you which passes are worthwhile and which aren't such a great value. That, of course, can depend on what sights you're interested in and how much time you'll have.
Keep an eye out for sales - look for signs saying oferta, promotion, etc.
