I would advise to go with as little as possible in your pack, so if you can avoid carrying an unnessasary pair of shoes, do!
I backpacked
Italy,
Austria,
Slovakia,
Germany, and some of
UK last summer and I had a great pair of sandals that I took for everything. (I assume you mean back pack travelling and not actually mountain climbing!) I'd been having major arch trouble with my feet just a week before I left, so on Dr. recomendation, I also bought a pair of insoles and took with me materials to tape my tha arch of my foot as needed. If that isn't an issue for you, you should be fine with just good sandals. I brought a pair of very light flip flops too just to wear on the train, in public showers, by pools, with a skirt, etc.
Have a great time! Enjoy all the sights. Get off the beaten tourist path (the best things we saw and the greatest expereiences were in the out of the way places!), make a difference in each place, and have fun!

Allyssa