Trying to think how best to answer this so forgive if it's a bit all over the place.
For context, my DC go/went to a prep that feeds predominantly into Canford, Bryanston and Claymore at 13+ ( grammars, Ballard and Talbot Heath at 11+). Generally, at 13+ the more academic kids go to Canford, then Bryanston, then Claymore, but there are some academic stars who go to Bryanston for the performing arts, location or they just prefer the vibe. Both Bryanston and Claymore are pretty academically broad - Claymore has very good support for SEN so results do reflect that. If you look up the GCSE results, you'll get an idea of the students they are admitting.
The vast majority from my DC's prep schools go to whatever school they go to as day students although Bryanston has flexi boarding and "day with a bed" which is now quite popular for DC that do a lot of extra curriculars (esp performing arts) as these can mean 9pm finishes. All three schools have decent numbers of day students although the arrangements differ in terms of how the houses work - Canford has dedicated day houses, Bryanston mixes them in, not sure about Claymore- it's the one I know least about- it's about 50/50 boarding vs day though.
In terms of playdates etc, they'll be past that as they'll be 13/14 but I know what you mean. Bryanston has Saturday school (lessons in the morning, matches in the afternoon) although Claymore doesn't, and most of the Saturday school kids just want to chill on Sundays as have had enough of each other! However, I think integration between day and boarders is pretty good at most schools. Even the day students come from a pretty broad catchment though which can make catch ups tricky - I know Bryanston day students from Christchurch and Salisbury. It's not going to be as easy as if they are at a local day school with a smallish catchment.
Preps- in the near vicinity, some of the preps that feed into Bryanston are Castle Court, Wallhampton, Dumpton, Sandroyd, Port Regis, Farleigh, Sherborne prep. But Bryanston does have quite a broad geographic reach as it's a "name school" so there will be DC from all over the UK and overseas, Claymore less so. Of course, Bryanston and Claymore also have their own preps so those are worth considering.
HTH. Depending on where you live might also consider Canford, although possibly you are the other side of Blandford.