I have a Canon Powershot SD1400 that I LOVE. It's nothing fancy, just an average digital camera but I love how simple it is and the night photos it takes. I bought mine on eBay since it's discontinued but I highly recommend it. It's my second Powershot and other than the first one being too big and bulky I have no complaints. And the battery lasts a long time. I had a Coolpix in between my Canons and wasn't thrilled, but I love taking night time photos and it just didn't suit me.
you can't go wrong with canon. nikon coolpix are usually good too.
read reviews. you can usually find reviews for anything on amazon.
One thing I do suggest- don't get one that uses regular batteries (like AAA), get one that comes with it's own special battery. yea you might have to buy a 2nd one (you can get some cheap ones are ebay) as a backup if your'e going on vacation.
if you do get one that takes regular batteries - you'll want to get rechargeable batteries (i learned that lesson the hard way... after going through a pack of AAA's in a few days)