Dolomite Spire is the finger-like spire between the Lighthouse and the Big Bend Butte, directly across from the Big Bend Recreation Area. It's about 300' tall looking at it from the river side, but only 225' from the other side. There are only two routes (that I know of) on the tower - the Kor Route (5.8 C2) and Dolofright (5.11d R).
Park at the Buffalo Chip Boulder (a large boulder immediately across from the towers). Cross the street and find a cairned climbers' trail to the base of the Lighthouse Tower. Do a short pitch to the notch on the right side of the Lighthouse (one or two 5.7 moves), then walk behind the Lighthouse to Dolomite Spire. Ascend one of two or three easy (5.8 or so) crack systems (choose whichever looks best) to the higher notch between Lighthouse and Dolomite. Begin the routes from a nice little ledge here.
Dolofright: a two pitch face climb up the blunt arete along the right side of Dolomite Spire as seen from the road.Begin from a comfortable ledge on the notch between Lighthouse Tower and Dolomite Spire (see approach directions for Dolomite). P1: Hard right off the deck. Climb up and right along an overhanging bulge (protected by three pins) using incut crimps, clip a bolt, and step left along a horizontal to the arete. If you found these moves difficult, get ready. ...[more]Browse More Classics in UT
Yes, it is possible to hike in from around the back. To do so, park at the group camping and follow the main wash until even with the Lighthouse/ main butte notch and then go up to Dolomite. This is a dog friendly approach, but the easiest is definitely from the front and climbing the 5.7 approach pitch.