As a Eidolon is "Summon once - hang around all day" kinda creature this makes me think of them as a perfect bodyguard. The Summoner is kinda squishy, so needs to keep melee foes far away. The working idea for my Guardian Eidolon is this...
1st level Medium Serpentine Eidolon - Evolutions: Bite (F), Climb (F), Tail (F), Tail Slap (F), Reach (Tail), Push, and Sting. Feats: Combat Reflexes
5th level Medium Serpentine Eidolon - Evolutions: Bite (F), Climb (F), Tail (F), Tail Slap (F), Flight (Magical), Reach (Tail), Push, Trip, and Sting. Feats: Combat Reflexes, Alertness, Skill Focus (Perception)
... given the example above, the idea is for the Eidolon to stick to the summoner like glue. Once flight is gained, the Eidolon hovers over the summoner ready to strike at anything that comes withing AoO range. Using trip or pushing tail slaps to knock back or drop prone any creature that gets too close to the Eidolons Summoner. Eventually, you'd pick up SLA that would grant invisibility or greater invisibility The Guardian would then hover silent and invisible.