What you need is some Macross, it set the standard for this combination. The balance of Cute Girls <> Mecha tends to shift somewhat towards cute girls as the franchise adds entries, depending on where your taste lands.
Some other choices that might fit the bill would be Full Metal Panic, Gunbuster/Diebuster, Code Geass, Brigadoon (if a girl meets robot romance is a side to this you're interested in), or Patlabor (if you don't mind your cute girls and mechs mixed with the buddy cop genre).
Depending on how exactly you draw the line for whats 'mecha', you could also go for unorthodox choices which are loaded with cute girls like Symphogear (girls using mecha-like implements to fight) or even Girls und Panzer (girls operating tanks).