It's one thing to live with your parents. It's another thing to be unemployed. It's another thing still to be unemployed and going off on cross-country trips, spending what little savings you have on frivolity. (I'm sorry, there just isn't a justification for doing that. "Finding yourself" is all well and good. But "finding yourself AND a job" = better.)
Penny is well within her rights to freak out. If it were me, I'd tell this guy he's got a couple months to shape up his life, and THEN maybe he can move in. He should be begging his dad for forgiveness and a room until he manages to get a job, and then start paying either his Dad rent, or, if he's lucky, he will have proven to Penny by then that he means business and he can start paying part of HER rent and living there with her.
It's ... actually pretty inappropriate to ask a brand new girlfriend to allow you to crash there completely for free. I really don't see how Penny is a bitch, just because she's suddenly been put in a situation where she's expected to take full responsibility for Wil in a financial sense. Since she doesn't know him very well (and we, as readers, don't know him very well), she doesn't know how motivated he is as a person to get a job and save money responsibly. Based on his recent behavior, he certainly does not look like the motivated type.
Apparently Penny is very careful with her money since she appears to live in a nice apartment entirely by herself, and all she does is work at a coffee shop. That would take some very fastidious financial management to pull off, unless Coffee of Doom pays ... unusually well for a coffee shop. If Wil doesn't approach his finances similarly, then that's going to cause problems later. I do think they can work it out, I just think Wil needs to shape up first and prove to Penny that he is worth it and NOT a lazy freeloader. If he works hard, he'll be able to show her this and earn her trust, and this fight can be left well behind them and laughed about later on. "Remember when you were a beatnik poet with no savings to speak of?" "Ha, yeah, but now I work at Whatever Library and I'm published in the New Yorker. Ohhh, those terrible days of my unpublished, impoverished whimsy! Thank goodness they are far behind."