My husband and I would like to stay in a simple, relaxed place maybe by the sea for 1 week, then we will stay with my cousin for another week, can you recommend a location that is not too expensive?
The Buranco Winery/Agriturismo in Monterosso/Cinque Terre would be my choice for that criteria. http://www.burancocinqueterre.it/ The wine and olive oil is amazing and the hosts were very kind when we visited. The rates were 60 euros pppd, though they made a special offer for a November booking for us of 100 euro. Monterosso itself is quite boisterous along the beach during the summer, however, so that may be a turn-off, though the vineyard itself is up the hill from town (with a great view, btw) I have heard great things about the Gargano peninsula, w/r/t being more peaceful but haven't been. Yet.
Do you have RS Italy Guide book yet? If not, you should get it as it has lots of information on places to stay and prices.