Within walking distance from the centre of town, I would head to the West Common, 10-15 min walk, Carholme road and keep walking, you will see the old Grandstand cant miss the expanse of grass!
Right down the end of the high street, near south park roundabout is the South Common. Plenty of space there as well.
On the way to Washingborough, near the Bowling alley and Crematorium is the cow paddle. Not good on Sundays though as its used for Sunday league football.
There is a field the otherside of the road from Hartsholme park. Football fields again but should be enough space for a fly.
I would say they are your best bets. Once I am up and running with a kite you are more than welcome to hitch a lift should there be any meets out on the coast.