I agree, a mile or two are good runs! I started off only being able to run 5 minutes and eventaully worked my way up to 30 minutes. But I still have my days when my body just doesn't want to work with me and I only run 10 minutes. But it's all good.
Since you don't want to be a 'runner', just focus on running for 20 minutes (or more if you can). It's a good start.
Congrats on the weightloss so far!