hitching to the north side of Balaton
You should walk to the north of town, following Palotai ut or Szent Florian Körüt. At the end of the town, there is a roundabout where the only main road on the north side of Balaton starts. Use a sign, saying Veszprem. Once you're in the rural areas you can hitch with a thumb everywhere, people there are very likely to pick you up.
hitching to Budapest from the north side of the Balaton
From Veszprem, Varpalota on route 8:
There is a bypass road east of the town, where the route 8 ends. There is a sign to the motorway (southwards): don't take that way, the cars all head to Balaton. To get to Budapest get through the city centre (maybe take a local bus), or take the northern bypass. Find the "Seregelyesi ut" or later: route 62 to Borgond (Börgönd), there is a petrol station on the highway, where 62 crosses it. The highway has much bigger traffic, I don't recommend the old road "7es ut, Route 7" with its mostly local traffic via the urbanized Velencei to/lake. Good luck!