This past summer in Spain, I took multiple weekend trips with a group of my friends from my school program. A great way to save money and energy while traveling is to travel LIGHT. Most trips were only about 3 days each, and I was able to fit everything I needed into one backpack. I never had to lug around multiple bags or suitcases, and I saved at least 20-30 euros on each flight by not checking a bag (it is not fun dealing with lost baggage in a foreign country). Most airlines have bag size requirements for carry-ons, but a modest sized backpack is usually within those limits.
Granted my trip was in the summer and required less/smaller clothing, but in winter months I would recommend wearing outerwear on the flight to save bag space (the cabins are normally chilly anyway). And when I would bring multiple pairs of shoes, I would tie the second pair together by the laces and string them through the loop on my backpack to save space.
Travel light: save money, space, and energy.
During the summer, I stayed in hostels almost every time I traveled. Most hostels have single, double, and group rooms for very reasonable prices, I would recommend booking a few weeks in advance to price shop as well as make sure your whole group is accommodated. The rooms with more privacy and access to bathrooms will typically be the most expensive, but still beat hotel prices most times. I would also recommend purchasing a lock, as most hostels have lockers for personal items (very convenient, nice to have peace of mind). I did not have many problems with hostels, and typically the other travelers were in my age range. The most useful service for finding hostels was Hostel World, you can view information and reviews and even book/pay for your stay. Their website and customer service are both great. I had a positive experience with hostels and recommend them, especially for groups.
In every country I visited, I used public transportation to get around in metro areas in a quick and convenient way. In Barcelona, rode the metro (subway) to save time and money. There are texis but the metro is much cheaper. You can get into the metro for about a dollar each time, and ride to any point in the entire city. You can literally ride the metro all day if you want to, once you are in then you are in. Usually, I would walk to my destination if it was within a few blocks or if I was not in a rush, the weather was great most days. The nice thing about the metro is that you can buy the passes in bulk, and you can also buy an unlimited pass for a month or multiple months. ALSO remember to keep your receipts for your passes if it is a large amount. If you lose your physical card you can have the staff print you a new one for free. The transit staff is typically very helpful and understanding, many people lose the small card that is used for getting on the metro.