Anyone have any holiday recommendations for Italy or Portugal?

So, I am having a terrible time planning a holiday for the BF and I. I have been looking up hotel/flight deals on Expedia and our budget is about £250 each(though he'd prefer £200 each). My head is spinning as I've researched about 10 cities so far! I guess it doesn't help that we are trying to go 2 weeks from now..

We want to go somewhere warm, beach, white sand, warm water, and not too much hassle with transport to/from the tourist areas, hotel, airport. I also want to go somewhere with a bit of history or sight seeing. Is that asking too much?  . The problem is most cities/hotels are out of our budget, or if they are in budget, they are too far from the airport, city center, and beaches. Ideally I would love to go to Lagos or Algarve, Portugal or an island in Italy. Though it seems that the cheaper options are bigger "touristy" areas on the mainland such as Rome or Venice, but all hotels in our price range are far from the city center and the beaches are even further.

Does anyone have any recommendations? I'm trying to stick to Italy or Portugal. Thanks!

We went to Madeira, a Portuguese island, for our honeymoon and it was wonderful.  My husband still has Funchal in his weather app and keeps torturing himself with how lovely the weather is there.  Downsides are lack of white sand or beaches, though they impressive saltwater pools like giant tide pools, with the waves breaking against or over the walls.

My husband spent the last couple of days looking at cheap holidays on Thomas Cook and we're thinking about one to a Greek island in September. I think your list at your prices is too much to ask for. Search for holidays in your price range and see how many of your other criteria you can meet.