I think that is a great idea! I have volunteered, observed, and worked in different PT settings but my employment was better than all of those experiences because I worked directly with the patients teaching exercises and performing modalities. This experience gave me a lot to talk about in the interviews and essays that came later when applying to PT school. And as you pointed out you do get to meet potential references for your application in this employment.
Hospitals and Outpatient clinics both hire PT Aides. As others have mentioned I too have noticed that after volunteering at a the PT department of a local hospital a job position came available within a month or two of my time there. I worked in an outpaitent clinic and found this position through craigs list. I don't know how productive just calling random clinics will be for you, my dad recommends it but he's old school
Good luck, sounds like you are on the right track!