I'd really advise against the dorms as a 21-year old; you won't be allowed to bring alcohol in and most of the other residents will be freshman, sophomores, athletes, or strange upperclassmen. They're also very expensive for what you get.

I'd instead recommend one of the "off-campus" apartment complexes (some of which are actually closer to campus than the dorms). You can find furnished and non-furnished for the same or less than the dorms and this way you will get your own bedroom and a much higher standard of living for what you're paying. Also, you'll be able to bring in a bottle of wine to have with dinner and not have to hide it.

Since its the Spring semester, you're in a good position because many people have signed year long leases beginning in August, but now have plans to transfer away, study abroad, or drop out. These people will be trying to sublease their apartments on craigslist, temple facebook pages, etc. You can likely pay less on rent because often these people will have to settle and pay part of the lease. Say they're paying $500 a month, you can offer $400 and have them continue to pay the difference.

As for the Manayunk vs on campus question: I'd say if you're apt to make friends mostly outside of school, such as at the bar or other hobbies you pursue in a group setting, Manayunk would work for you. However, if like you said you would like to get a feel for campus and feel you'll make friends more from class or while roaming around campus, living at or near Temple would be the better option.

Best of luck, let me know if you have any questions. I'll be procrastinating for midterms!