Conserving hunger while running?

Good question!

As it so happens, the Minecraft Wiki happens to lay this all out in a nice little table:

Method of Transport             Exhaustion (Relates to Hunger) per block

Walking                         0.01
Sneaking                        0.005
Sprinting                       0.1
Sprinting while Jumping         0.8

Since this is all per meter, we can see that sneaking is the best. While it may be slow, it does actually conserve the most hunger. If that is too slow for you, use walking. Also, running and sprinting a little back and forth won't work too well.