Fun things to do in Rome?

Hey guys i’m in my mid-twenties and headed to Italy for the first time in a couple of days and was wondering if anyone could recommend some good places to visit for sightseeing, eating out, socializing etc etc

I am a vegetarian so if you guys know of any restaurants that provide a good choice for vegetarians that would be fantastic

I will be staying at the Hotel Aniene so anything close by would be a plus but im going to be traveling around as much as possible so anywhere that’s reachable with public transport would be great

Also if you have visited and had some great experiences please do share and perhaps some recommendations on days out would be great

I have a keen interest in photography so i will be taking my camera with me everywhere i go, would love to be able to see some of the amazing structures and perhaps some night shots that really capture the city so if you guys know of any amazing spots for photographs leave a little comment or perhaps even some photo links