Temporary summer housing (Amman)

Hello - I am a student studying Arabic at Qasid in Sports City for the summer (mid-June to mid-August). Qasid offers housing, but it seems overpriced. I've studied in the Middle East quite a bit, but have usually opted for university housing, so this is my first time apartment-hunting on my own.

I'm coming by myself, so I'm open to studio or 1BRs or finding a roommate. What's the best way to go about finding an apartment for the summer? What is a solid budget (I'm not looking for anything too fancy, but will have to get to campus everyday)? Are there any neighborhoods that are unsafe for young females living alone (or even with a roommate or two)?

Thanks for your help!