I've been working on choosing a blue color for my house--and there are a lot of blue-green paints out there (some with gray undertones). You might try working with those at the various paint company websites. I think that color can be tricky, but it might work for both your blue and green pieces.
Check out the Home Deocorating site, too--lots of people can give advice on the colors that worked for them!

I think a neutral cream shade like SW Ivoire would be a good backdrop for both decors. You could always go basic beige like SW Kilim Beige, but I think Ivoire is more cheery and warm. I have Ivoire in my living room with blue rugs and chairs and it looks very nice. It goes well with green as well.

SW Blonde is a very popular neutral yellow/gold-similar to Ivoire but a little darker. But in a bright space, Blonde can really look "gold" rather than neutral. I have it in my formal dining room and most of the time I really like it, but when the afternoon sun comes in the bay window, it looks really gold. In the evening when you're most apt to use a formal dining room, Blonde looks great. But you might want to take a look at it as it's one of SW's top selling colors and decorators use it quite a bit.