FSM controller failed to issue timely turns to a LOC 34 inbound aircraft resulting in a MVA infraction; the reporter indicating misapplication of priorities was the primary causal factor.

Narrative

North flow; ER and WR combined; a more complicated flow; but visual approaches were working with a ceiling at about 5000 feet. Aircraft X on RADAR vector for a LOC 34 approach to Runway 34 at 3000 feet on a left downwind. I had several things I was trying to accomplish at the same time; but all were routine; except an inbound that distracted me; an inbound to an airport the computer said was in my airspace; but I didn't recognize. The inbound was on an aircraft; IFR to MU98 (I do not recall ever seeing this airport before). Aircraft X was nearing a point where I needed to turn his base but I thought I had time to check the location for the unusual inbound and still get back to turn the T6 onto base. What I didn't realize was that the T6 was faster than usual due to an apparent tail wind. This caused Aircraft X to enter a higher MVA area (sooner than I anticipated) just as I looked back to turn his base. I immediately climbed the T6 to 4000 feet and turned Aircraft X out of the higher MVA area. Had I noticed the speed gain I would not have missed the turn to base and would have prevented the T6 from hitting the boundary line of the higher MVA area. Recommendation; this was; simply stated; a misapplication of priorities. The distraction was not a time critical situation as the base turn was. I was trying to accomplish too much with the available time; particularly when I take into account that I allowed my curiosity to control my judgment of priorities.