Hello Elizabeth,
Although this might be a late reply, posting this here for future reads.
Socializing is one of the easiest things to do in Tirana, depending on your age and location and one of the hardest things to master.
A young person, located inside the city's urban area will have a far easier time than an older person located in the suburbs.
The Albanian youth speaks good English and weirdly enough, good Italian. People are outgoing and will talk your ear off if you give them the chance.
The opposite is true for most of the older generations, their English is lacking or missing altogether and their friendliness tends to go down a notch (not the norm).
I'd advise you to go out a lot, people will oftentimes start conversations out of the blue, asking you where you come from etc. I'd make friends out of the ones you like, as you will need their insight. It is really hard to find a group with similar interests in Tirana, you can't search online for meetups or groups, and information is really scarce.
Your best bet however would be finding similar people in your position (other interns from abroad) as they have gone down this road before, or will be willing to join you in your search.
Now to more specific stuff regarding your interests, food and exploration.
Food and Drinks - one of the best things about Tirana in general is eating/drinking out. Great cuisine affordable by anyone. However as you may have seen quality and quantity is never a problem, variety is. The vegetarian restaurants can be counted on the fingers of one hand. I'd suggest following local pages, one of which is HaPiTirana, which does restaurant/bar reviews and as far as I know is managed by expats, one from Australia and one from Germany.
Outdoors Exploration - same as above, not much variety here. Lots of exploration groups, most of which offer hiking expeditions. I can recommend one, Klubi Discover Albania on whose guides I have been a couple of times, but can't really talk about the others. Something to note here: the participants are all locals and the guide is in Albanian, so you might want to make friends on the way there (bus trip) in order to get some translation/sense of what you are doing.