You are stronger than I am (USCF 1800+ at the moment), but I've played the double king pawn for some time. If you're looking for how to defend the Ruy Lopez, I really think that the mainline Chigorin is the way to go, because it practically forces the game into typical patterns/plans.
I have also learned a lot about chess in general by taking up the Classical (Cordel's) Defense - specifically the Berlin classical (3...Bc5 4.c3 Nf6 or 3...Nf6, 4.O-O Bc5 being the most likely lines), and I've learned a great deal about complex tactical operations and material compensation by playing what I've seen referred to as Moeller's Defense (3...a6 4.Ba4 Nf6 5.O-O b5 6.Bb3 Bc5).
I imagine the Breyer is the way to go if you want deeper strategic play and more options, but I've only played it twice and both times were odd opening crushes because my opponents self-destructed. I doubt that will happen with opponents rated 2000+.
Incidentally, the best discussion of the opening I have ever seen is in Suetin's book _Modern Chess Opening Theory_, from the point of view of offering ideas on how to conduct a course on the development of the opening's theory.
What 1. e4 e5 opening as black should I play to get better? I am approximately 2000 USCF and I would like to step up my game. I am not so much interested in winning so much as exposing myself to essential positions so my game improves. In the past I have played the sicilian as black but I am switching to ... e5 since I have never played it before so it would be a quick way to improve since I am seeing patterns I have not seen much before. I tried main line ruy lopez as black with the ... Na5 and ... c5 move but I have hard time winning with it and even lose against weaker players. Anyway, my goal is to improve, any openings some strong players recommend?