Rhode Island is a solidly blue state, but we still tend to elect Republican governors in a weird kind of check and/or balance. While it manifests itself in presidential elections, locally people are lot more divided in political philosophy.
Nate Silver did a really cool analysis on a phenomenon he called “elastic states” of which Rhode Island was number 1 in elasticity, and explains what you’re talking about. I just read it this morning and thought it was one of his best articles. You should go check it out on the fivethirtyeight blog.
Also, I live in Texas which is a solidly republican state, but probably only for another 10 or 20 years at most.
As a state, where I am is solid blue. The town I live near is really solidly blue. Out in the sticks where I live, it’s pretty damn red.
New Jersey. Solidly blue. For governor it will swing back and forth. People dissatisfied with what is going on in the state economy tend to blame the guy in the statehouse. But nationally it is very rare for it to go Republican. Except in a couple of landslides. Also in elections for Senate it is firmly Democrat. There are some areas that are more Republican and there are some Republican Representatives. The roots of that are back with Frank Hague and the corrupt political machine in Jersey City.
Illinois is pretty blue for presidential stuff but about fittyfitty for governor and US senators.
Swing but we (barely) went blue in 2008. I think this year we’ll probably go red, but barely.
Pennsylvania. Philly, Pittsburgh, and a few other smaller areas are blue. The rest is red. We’ve gone blue in the last few general elections, but then again, we’re also responsible for Rick Santorum. Sorry about that.
liz-Apology accepted. 
BTW, I’ve heard PA described as: “Philly in the east, Pittsburgh in the west, Alabama in the middle.”
I live in Missouri. St. Louis, KC & Columbia are solid blue. The state as a (w)hole is decidedly red. 
It’s also been called Pennsyltucky