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What are the best websites for Travel deals for Europe and the other side of the world?
You might want to try travelzoo.com. They let you search through multiple sites. If you are talking about Ireland, try aielingus' website. For the UK, go to ba.com (British Airways).
Websites like travelzoo or bookingbuddy - there must be dozens of them, will let you search multiple sites at one time and multiple airlines at one time, BUT I found by using that as a guideline and then going directly to the airline site and looking up the same info, I got cheaper flights. Happened more than once for flights I booked on Delta, Aerlngus and Airtran.
If you're looking for tours/hotels and other stuff - not just airfare - for Europe try Dooley - can't think of the rest of their name right now and Sceptre Tour or Tours, Aerlingus also has hotel/air deals all over Europe on their website.