Lydiard Park is a large manor house with landscaped grounds, run as a country park by Swindon Council. Just off the motorway, it's a really convenient place to meet up, with free parking and access to the park, cheap food and toilets, but it is also "worth a detour" in its own right.
The park has something for everyone. For kids there is a large play area, aerial ropeways (paying), large lawns for running around and picnic areas. For adults, besides lovely lakeside walks, there is a medieval church, walled garden and 18th century house (£4:70 for house & garden). These far surpassed my expectations. It's well worth the bother of collecting the key to the little church from the reception in the house - it is unspoilt, with huge Jacobean box pews, wonderful tombs and fantastic painted wall panels. The house has been extensively repaired but is well worth a visit. The plaster ceilings are lovely and the council has recovered a huge collection of family portraits which were sold off in times gone by. The rooms are well-furnished, with realistic dressed figures to bring things to life and helpful audio-panels that include a button for the kids.
For a quiet visit, follow brown signs to the house and church. There's a good café in the stables, serving soup/sandwiches etc. or the conference hotel will whip you up a fantastic granary sandwich to eat in the bar (£5:50 for pot of tea, sandwich, crisps & side salad) The public toilets are immaculate.
For family, the country park signs take you to a car park near the play areas. There's a bigger café here, better for buggies, but it can get very noisy & greasy.