I have some other comments, based on the others' advice here:
1) der Kluge hit something vital: a good DM caters to the tastes of his players (not the characters, the players). Your group may be inexperienced enough to even know what those tastes are, yet. But after trying some fight scenes, some poltiical intrigue, some exploration, observe and think back to what things "light up" each player, and remember these. Some players are happiest in combat, or power accumulation, or both. Some are happiest when they make intricate plans that succeed without a hitch. Some are happy just by having their character shop with the general store owner for an hour. Find out what drives your players, including yourself as DM, and give each one a brief chance to shine.
2) There are some games with some quite innovative systems that replace or supplement combat: Spycraft 2.0 from AEG, is a good example. Its nicest new contribution to d20 games has been conflict resolution; it gives rules as beautifullly complex as the combat rules, and applies them to everything from chases, to brainwashing, to manhunts, to interrogation, to even seduction. Taking that vein, where what makes combat "combat" is the complex dance of tactics, dice rolls, and multiple small resolutions, Spycraft makes even things like interactions have some vibrance other than a single contested roll. E.N. Publishing's Tournaments Fairs and Taverns had a similar concept, but not as fully developed.
3) If this is the first time DM'ing, take it slow and simple - no need to try to craft some massive political intrigue or complicated combat, or massive dungeon exploration. THe biggest goal is the fun that comes from socializing with friends while creating a shared adventure together, same as anything else you do with friends. Dungeon magazine has a large number of adventures with a good mix of combat and involved plot that you could get the group's feet wet with.
Good luck in any case!
P.S. Nitpicky point - though Vampire's Mind's Eye Theatre Live Action Roleplay products does have some "rocks, paper, scissors type resolution, the tabletop version of the World of Darkness stuff does still use dice for resolutions (d10's).