One option that I've seen work well in other games is:
Abort-to-Dodge. When an enemy that you can see attacks you or forces you to make a Dexterity saving throw, you can Dodge as a reaction, but then on your next turn the only action or bonus action you can take is to Dodge. You must declare the Dodge before the attack roll or saving throw is rolled, and the Dodge applies to the attack or saving throw.
(rephrased into 5e terms)
I very, very rarely see the Dodge action taken, and I think one of the main reasons is that you have to be really good at anticipating enemy actions in order to perceive Dodge as worthwhile. Allowing it as a reaction means that when you suddenly find yourself staring down the barrel of a Huge-sized greataxe you can chicken out and just Dodge. Pwhew!
It also reduces the feeling of helplessness when you get attacked. Enemy spellcaster coming at you with some nasty touch spell? Now you can actually do something about it! It's costly because it eats your next turn, but, hey, PC's gotta live.