There are charter flights from Helsinki, Moscow, Tallin, S Peterberg, Paris and Bacu. These flights are all to Ovda which is one hour away from eilat.
There are many many flights that go all the way to Eilat. They are operated by Arkia or Israir. You can fly from TLV just change to terminal 1.
Many other flights go from Sde Dov airport which is actually in Tel Aviv.

I would do a third option. Come to Israel, and in the middle of your trip go for a few days to Eilat.