K.R.
There is extensive info on all the Portland Public Schools, including magnet programs. They have links to the public charter schools (public (free) alternative-model schools).
It looks overwhelming, but if you start with a search for your neighborhood school (enter your address, it should tell you), you can see if your work will be easy (you like that school) or if you will need to put in the time to research and apply to others.
I thought interesting the Chinese/English immersion school in SE, the Creative Science school (also in SE last I checked), and several of the charters (there are only 7 charters right now, so they are pretty quick to get through).
Picking up Portland Parent magazine (free around town) or buying the Portland Monthly schools issue (I think it comes out in the spring) can expose you to a bunch of private-school ads very quickly. And of course, there's always the good ol' yellow pages, which can tell you what search terms to use in Google to find local private-school websites.
We had a child at a parochial school for one year (this showed me how much I disagree with standard academic schooling, no matter how lovingly pedagog'ed), and a child at Cedarwood School for one year (this was expensive but utterly vital for that child; Waldorf education is the most truly developmentally appropriate curriculum I have run into).
We were blessed to get into, and are happy to be at, Portland Village School, a Waldorf-methods public charter now in its second year.
I do have to say about charters, though, that they come up for renewal every three years, and that built-in uncertainty is a bit stressful. On the other hand, it's not like the public schools haven't been reorganizing about every three years, too ...
Anyhow, hope some of that helps. It seems like a big process, but once you start reading, a lot of options will drop away and that makes it easier.