1

I was there in June last year. From July on, I think most or all the routes will be feasible. Even in June, there is already enough choice.
Topological maps are sold by Geoland in theiur shop in Tbilisi. They are not very good. Some trails are marked, but don't expect too much.

2

Do you have already certain route in mind? Basicly the best time to hike in Svenetia is mid July - mid September.
Although earlier is also possible but weather is less predictable.
I would go through Chauhi pass (near Kazbek). In Svanetia there are plenty of routes although trails are not as well marked as in Europe. Mazeri and to the Ushba Glacier is much more rewarding than Chalaati Glacier (one day hike). With tent you can hike to Ushguli from Mesia. Without maps (some basic maps are easily found in Georgia) you can easily travel in Svanetia unless you go to more secluded places, which I wouldn't recommend as most good maps are in Russian and it is easy to get lost.

3

Also Guli Pass which goes from Mazeri to Mestia is also very spectacular. Unless you climb very high passes snow is no concern strating from mid June. but again, weather is better in August or second half of July. Maps are available in INFO Center in Mestia.

4

Thanks for the advice, we've decided to go from early Aug to early Sep in the end. Thanks for the advice on the hikes; we don't have anything in mind yet, but our general philosophy is the more isolated the better. We're use to multiday trips through the Canadian rockies where you don't see a single other person the whole time, but we can also easily understand the maps there, maybe we won't be so brazen in Georgia...