If you don't like making your own espresso, or want to get outside, there are a couple of good nearby coffeeshops.
- Stellas (in collegetown, across from the Starbucks) has very good brewed coffee and tea, and is a nice place to sit and work.
- Cafeo serves Gimme! coffee (a local coffeshop/roaster), but doesn't have very much seating and the quality can be hit or miss.
- If you just want coffee on the run and don't particularly care about taste, Collegetown Bagels (CTB) is the go-to.
- There's also coffee available in the downstairs 'cafe' in Duffield, but the quality is generally pretty poor.
If you want to come drinking with the PhD students on Fridays, sign up for TGIF: 
If you want lunch companions, send an email introducing yourself to the social mailing list. It's also a great source of information about local events/happenings.
Student visitors: come to Student Brown Bag on Wed (during the year) to find out about the research going on in the department.