Good primary and secondary schools, as well as community feel. We wanted to cut down on our commuting and walk to school/into town as much as possible, whcih meant that we had to compromise - a modern house in the sort of locations we like was affordable, whereas a character-filled Edwardian house was not.
The school run can be knackering, but walking is much more pleasant and less stressful than driving and having to find parking.
For us the heart of the home is the kitchen-diner, particularly as it overlooks the garden and has doors into other parts of the house so isn't isolated.
Sacred adult space can be created by the clock, rather than physically. We do have a study, but as the older dc use it to take refuge from the toddler when they want to play with fiddly or fragile precious stuff, we only get to use it after they're in bed. OTOH, as the toddler gets older perhaps we'll be able to teach them to respect each other's space - as well as ours!
Bathrooms: having two is brilliant, as long as you don't mind the ensuite being available rather than being your haven. More than two would be too much cleaning IMO.
Garden is useful, but size not necessarily critical. Though you might have the sort of boys who really need to kick around freely. Or maybe a nearby park would be better. Outdoor space of some sort is imporant. Also should not be too precious to you, at least at first, so that you won't feel gutted when they trample your bedding plants chasing after that football, or rip up the daffodils to give you a "Sorry" bouquet.