Ciao Linda,

if you could be more specific on the budget I can give you some suggestion about some nice hotels near Capri, Pompei. June is a perfect period to visit the area and Italy in general, very nice weather and not too crowded!!!
In 4 weeks you may consider visiting a part of the Alps, I would suggest Dolomites, they are really different from the US mountain landscapes. Go discovering small towns in Tuscany or Umbria, like San Gimignano http://www.sangimignano.com/sghomei.htm
In south Italy, Salento area is very nice!
There are a lot of possibilities and very nice spots!!
Please fell free to email me if you need any insider tips

BR

Matteo