Harrold Country Park - some nice options for lunch and snacks are served at TEA-ZELS cafe - alll fresh, homemade, and very tempting! The cafe is open 7 days a week from 9am to 4pm (5pm in summer and at weekends) - see http://www.hocp.co.uk/about-hocp/
The park has a pleasant circular walk/ cycle ride around the lakes, and there are plenty of waterfowl and birds to see. There are large open spaces that lend themselves well to kite flying, and of course, an ice cream van.
See also http://www.harrold.info/busserv/food.html For other food outlets in and around Harrold.
Irchester Country Park - a little further away towards Wellingborough is this former ironstone quarry. It has a wonderful children's play area right beside the popular QUARRYMAN’S REST CAFE, where they claim their food is fresh, healthy, tasty and local http://www.quarrymansrestcafe.co.uk/Quarrymans_Rest_Cafe/Home.html Delicious cakes are served here at reasonable prices - the cheesecake, pictured, is a good example of the portion size, and it's very tasty too. The park has a network of long and short trails through 83 hectares of mixed woodland. Irchester is close to Wellingborough, a small town with a distinctly midlands feel to it, and plenty more food outlets - see
http://www.thebestof.co.uk/local/wellingborough-and-rushden/business-guide/popular/food-and-drink
Emberton Country Park - originally a gravel works, now an attractive 200 acres parkland setting including two lakes completely circled by a cycle track. Be cautious on bikes, though, as this track is also used by slow moving car traffic. If arriving by car, you have to pay to be admitted, but it's free for cyclists and visitors on foot.http://www.visitolney.com/Emberton-Country-Park Sadly, the cafe provides only limited fare, mainly drinks and sweets. Since there is plenty of space for picnics, and the park is only a short walk from Olney, the best option is probably to pick up something tasty in Olney and enjoy a picnic. http://www.visitolney.com/welcome