http://www.nationaltrail.co.uk/southdowns/sites.asp?PageId=40
Have a think about how far you want to cycle out of your way, though. And bear in mind when you look at the map, that a place might be 1 or two miles from the trail, there might be quite a bit of extra altitude in that distance. I’ve only stayed in the hostels before, because I’m a lazy cheapskate.
Handiest options for least additional miles are a 20 mile afternoon on the first day, (Assuming you’re going West – East) stay at East Meon hostel, right on the trail, 40 miles to Truleigh Hill hostel, right on the trail, and 40 miles to Brighton on the last day.
You can get takeaway delivered, and/or send someone out for ale. Or take a taxi to a local pub.
Oh, and welcome to the forum! There’s plenty of advice on lots of threads on here about the SDW, try the search box or use google. The bikedowns(.org?) site is well worth a look too.