Mestia is not a large town and can be walked out of easily. It has the major Svaneti road running through it. It also has a road that splits off to the north toward the border with Russia (closed now for many years) and a trekking trail to the Lekhziri glacier.
Mestia can easily be walked out of to get onto the Svaneti road. If you watch the road markers you can make sure you are heading the right direction. The markers are skinny white poles with two square blue plaques declaring the kilometer distances to the ends of the road. If the number facing you is around 140 then you are heading to Ushguli and Lentekhi. If it is around 65 then you are heading to Zugdidi.
On the way to Ushguli there are some other settlements, it's not a totally deserted road. However the traffic is lower than to the west, it is possible to hitch there within half a day. Road is poor and only jeeps or SUVs can cross. As for sleeping, also for find a lift, Mestia and Svaneti region are harder than the rest of Georgia. The development of tourism made local see foreigners just as a source of income and the absence of local public transport made them work as taxi substitues especially beyond Mestia (Ushguli and all the road leading to Lentekhi), thats why most often the best option for hitchin are tourist groups with their own jeeps or ur humble legs.. Fede as other hitchhikers (Jo, Alfie and Emee) has been asked for money more than once. generating surprise and disappointment after being accostumed to gorgeous georgian hospitality.
The inhabitants of Mestia have become accustomed to the tourism economy and staying in local people's homes for free is not common (the traditional Georgian hospitality of the lowlands does not exist here). Homestays are expensive, at least 15-20 lari/night. Camping is possible outside the centre of the village, but ensure you have proper cold weather gear if camping in winter.