Take the M3 motorway from Budapest as far as Hatvan, then take route 21. Before Pásztó the road branches off towards HollókÅ.
There is a bus from Budapest leaving from the main bus stationdeparture 8:30AM, Arrival 11:00AMreturn 4:00PM, Arrival 6:30PM
Eger might be close to HollókÅ, but it's not a really good place to start your journey to HollókÅ if you plan to go by public transport. There is no train, and you need 3 buses that are going to take a total of 4:30 hours to get there... Eger information centre can help for time table and details.. Prefer a departure from Budapest or GödöllÅ