Alternatives to Starbucks
Wow you received excellent recommendations. Rays is a good choice if you want a spectacular brew their blue mountain is as good as the best of Jamaica and the Kona is a s good as 5 star Hawaii. Old City is also excellent. If you think your cafe has more elan with a whiff of BO Colombe is your spot.
Old City Coffee 221 Church is an excellent spot for a visitor. Trendy neighborhood near historic stuff, nice architecture, and you can walk anywhere in town from there or hop on the El. The spot in RTM is also an excellent place to grab a cup.
What a fun topic! Aside from some of the ones named, in university city I like GreenLine Cafe on umm 43rd adn Locust I believe and Brew Ha Ha on 12th and Locust (that location might not be right so I apologize) is great for sitting down (comfy chairs!) and even having a scone or muffin.
Places for a good shot of espresso:
Stellar (10th and spruce)
La Colombe (19th and Sansom)
Joe's (10th and Walnut)
Haussbrandt (15th and Walnut)
Places to have a shot of espresso, then sit and hang out:
Philadephia Java Company (4th and Lombard)
Chapter House (9th and Bainbridge)
La Colombe, again
Plenty of others are good, too, outside of center city (incl. Chestnut Hill coffee, which is good but a bit overrated IMHO, and varies a bit too much barista to barista).
If you're staying someplace outside of center city people can probably give more specific advice.
I don't really like other drinks (brewed coffee, drinks w/milk) so I can't say anything about what they're like from one place to another. Good job staying away from starbucks when there are so many better options.
The best I've had in Philly to date is at Chestnut Hill Coffee. But that might be out of your way, so I'll suggest Spruce St. Cafe, corner of Spruce and 11th. They're still in "soft opening" until the 15th. They are serving Counter Culture Coffees and their espresso machine is a LaMarzocco GB5.
the northern liberties neighborhood oozes coffee shops. all of these within about 1 sq mi:
coffee house (on girard, near el stop)
one shot (in liberties walk, between 2nd and 3rd)
euphoria (2nd st in the funky 5-story building) - addictive pretzels
elixir (2nd street, just south of euphoria)
arbol (2nd and poplar)
higher grounds (on 3rd st) - great lounging area - my personal fave, even though i love em all
random tea room (4th st) - they do french press coffee
i put them in an order that you can literally do a coffee bar crawl walking for approx 1 min between most of these! don't know if your travels will take you up this way, but it's a short walk / 2 min drive from old city (where most of the historic sights are). just google the zip 19123 to get an idea of the area. i really love all the coffee options northern liberties has to offer. :) oh, and you can find a great brunch in the neighborhood, too.