There are Central Bus Station of Eged and Airport in Eilat. All day many buses depart to Beer-Sheva, Tel-Aviv, Jerusalem and Haifa. To Beer-Sheva is about 3.5 hours, Tel-Aviv - 5 hours, Haifa - 6.5 hours, Jerusalem - 4.5 hours. I like very much the road to Jerusalem. It goes lengthwise the beach of Dead Sea and is very, very beautiful (webmaster's comment). 
If you want to arrive to Taba - take the bus number 15 from the Central Bus Station.

 Another way to arrive to Tel-Aviv or Haifa is by plain. You may fly by one of the two airfly companies: Arkia or Israir. The flying time is about 50 minutes to Tel-Aviv and about 1.5 hours to Haifa.

And, of course, the car. There are two roads from Eilat to the North. One of them (number 90 or Arava road) is the main road and goes via Park Timna crossroad (about 20 minutes from Eilat), Kibbutz Yotvata and Yotvata Hai Bar (about 30 minutes) and some other interesting places. Another road begings near Shahamon District of Eilat, goes via The Red Canyon (about 20 minutes from Eilat), Faran Wadi (about 1 hour), Mitzpe-Ramon (about 1.5 - 2 hours) to Beer-Sheva (about 3 hours).
In Eilat one of the most easily way to arrive to any place is by taxi (inside the town is about 9 - 15 NIS, 2001).