Two miles? That's terrible, it makes me feel spoilt for choice. The nearest park is less than 5 minutes walk, and I've never really used it before D was born (we moved here nearly 9 years ago).
It has a cafe but we've started to get takeaway drinks from the cafe as in this weather I can sit on a blnaket on the grass with D and he can wriggle freely. He's not quite ready to be sitting up but he likes to be able to move about and he enjoys it more I think than lying in the pram or on my lap. And he's not too mobile. And I'm not worrying about exiled smokers sitting too near my baby or me (plenty of space in the park).
I've learned that this works well from meeting up with my NCT classmates at Highgate Woods - we moved from the very crowded cafe outside seating where we had to keep moving buggies so people could get through to the grass.
We did find discarded gluey bags and other signs of solvent abuse though, so I guess we'll have to be quite alert when he starts to crawl and toddle.