new england in may isn't that cold - but it is the start of black fly season (mutant mosquitos)- depending on how wet the thaw is - if its a mild winter... then it's not bad.
Going back to New Hampshire and/or Vermont -there's tons of day type hiking trips - especially in New Hampshire's White Mountains - theres one called
Rattlesnake -- it's a few hours hike - and an easy hike at that - sneakers and a bottle of water are all that are needed -and a picnic lunch when you reach the top - and you're greeted with spectacular views of Squam Lake
If the black flies are out -- a can of deep woods off is helpful -
While new england is absolutely beautiful - from Ohio - it's a quick trip thru PA and settling in the area around New Hope - which is ont he jersey border -it's a really lovely area -lots of antiquing - restaurants - bed and breakfasts and inns - plus white water rafting is nearby and may is a great time for rafting - you get the best rapids