Hostels verse Hotels verse AirBnBs.
Hostels: My plan often is to say at hostels because they are very affordable and in my opinion offer more than most hotels for the money. One site that I have used again and again has been HostelWorld.com. Their site is user friendly, and their customer service is great if you do find yourself needing assistance. When I look at hostels I usually get a private room either single or double this way I have my own space similar to a hotel, however I also get to be around fellow travelers who I can share stories of our adventure and get great advice. Many of these hostels are rated very high and even offer bonus things like free breakfast, and laundry facilities on-site. While I can say it can be fun to have an adventure searching out one in a foreign country it can also be nice to spend that time searching for something great to eat or see. Hostels often offer tours similar to hotels as well or know where you can go to obtain one. There are things to be aware of with hostels. Many of them you will have to share a common bathroom with several rooms either down a hall or on the floor your are staying on. ALWAYS bring some simple flip-flops and your will be fine. Most of the time you either are provided a towel or you can rent one from the hostel. I tend to bring at least a travel towel which is also useful at the end of the adventure if your have something breakable. The other benefit is that unlike a hotel you have the use of a kitchen if you wish to cook or even store food.
Update for Staying at Hostels - So things have definitely changed in regards to staying at Hostels. The largest change is the huge increase in cost. As I stated before I have enjoyed the different benefits of staying at different hostels. Its is great to have other guest to chat with, and a kitchen to use and other great resources, however the price increases have made booking an apartment or similar option just as desirable due to both options being similarly priced nowadays. I do hope that prices become more budget friendly again, and I do understand that Hostels are a business and need to make a profit while covering their overhead. I merely feel if I am going to be spend the same amount of money and I am able to get a larger space that offers more privacy and many of the same resources I have my preference.
Airbnb: That being said I have stayed at Airbnbs as well during several of my adventures. These can be great if you want more space and you feel exploring on your own is part of the adventure. I stayed at airbnbs when I was in Vienna Austria, Dubrovnik Croatia, and Budapest Hungary. They were all nice places to stay while I will say my stay in Hungary was a bit small. I will say you can sometimes rent an Airbnb for cheaper than you can a hotel and have more flexibility in certain aspects.
Hotels: Hotels can be great if you are only staying a day or two somewhere and are looking to treat yourself. The other benefits to staying at a hotel can be they can often set up tours for their guest as well you usually get your room cleaned daily. Similar to Hostels you can ask the front desk person suggestions, however be aware that often these hotels are in partnerships with certain touring companies and this will skew their suggestions.
Update for Hotels - So as with everything else the prices have increased to stay at a hotel. That does not mean that you are unable to find a great deal and still stay close to all the attractions and local transportation.