What is the best weapon to use againsted blue dragons

That depends if your a member or not, if you are you should probably use a "dragon longsword" appx. 100k. If not a "rune battle axe" appx. 50k.

It all depends on your plan of attack.

The most common way is to use range. Get your Blue D'Hide armour and grab a magic bow, be sure to take a lobster or two. You could also switch it up for a crossbow and antifire shield, or perhaps a prayer book for that range boost. Remember to bring your accumulator.

There are 2 areas with blue dragons with safe spots that I know of.
The first is in Traverly Dungeon. When you go through the gate into their enclosure, go right andalong the cave wall, you should come across a dargon egg and a couple of stalagmites within close proximity. Stand a fair bit back and range away, be careful of the baby ones though as they sometimes wander around the back.

The second spot is under the Heroes' Guild. When you go through the gate, run as far as you can to one of the 2 sides. Hide behind the skeletons and range away, although at peak times it can get busy and there can be a bit of contestation between players.

Well if you want speed, choose the scimitar. If you want power, go with the battle ax. If you want defence, go with the long sword.