This was one of the first games I ever got for my PS3 and it was my first foray into Western RPGs. I did pick a great game to start off with too. This game became my passion for 200 hours and I haven't even done everything.
Let me start by saying this game really sets the mood. It's a post-nuclear Washington D.C. and you are just a lonely person who has left the only home you have ever known in search of your father. You come to find out that the world isn't as empty as you once thought and it sets up a great adventure. This game has so much to do and see that you may find yourself just wandering for hours.
Sure the PS3 version had a number of glitches and it would crash often but it was still playable. I purchased three DLC for this (Point Lookout, Broken Steel, and the alien one). Each was well worth the purchase. This game was just so much fun to explore and do things with. Each place you journey to can have any sort of treasures in it that you just wander for hours trying to find the next piece of interesting loot.
If you have access to anything that can play this game, I say play it. It really shows how an open world should be, open. There is nothing stopping you from getting all the map points before doing all the missions or at least I didn't run into something stopping me. It's great to just wander around and make your own way.