I started watching this year, and I enjoy it. It is a bit overhyped by some, but it's quite good. A few dull races, as with every series, but the last race at Mid Ohio was great, it was a fight down to the last lap.
I think the ovals are almost always exciting (though, occasionally, you do find one that someone runs away with), but on the road/street side...ultimately, it's still road racing. Sometimes someone rips off into the distance at the start and never looks back; passing is very challenging even with the aero improvements (and, thankfully, NO DRS!) - but I kinda consider that a good thing. But, with the element of refuelling, even the more formulaic races at least have a couple moments of "hmm, this would be a really good/bad time for a full course yellow..."
I think a lot of the hype factor comes from us crossover F1/Indy fans who have suffered through a LOT of predictable F1 races and championships as of late, so we are like kids in a candy store when we watch even a mediocre Indy race!
And @Ryno917, thanks for the tip - I splurged for the paddock pass