Is there any place where beginning partial mods are posted for critiquing and suggestions?

There isn't a specific spot really. If you want you can make a WIP thread in the mods section of this forum. Or, if it's far more minor you can probably just make a thread here and ask people for critique. I'm sure some people will stop in and give it a try.

What kind of mod is it? That will affect (Somewhat) how much feedback you get.

It's a very basic room addition. It's mostly esthetics that I have questions about more than "how to's". There are so many choices it's kind of overwhelming.

Tes Alliance has a testing forum if I recall. Haven't been there for a while.
If you think your mod is almost ready for release, submit it there and people will bug test / recommend changes / etc.

If you have a Steam profile, a few of us set up a Creation Kit group on Steam and we have an area where you can post information about your mod and get some feedback.

http://steamcommunity.com/groups/SkyrimCKPublic/discussions/0/882957626002618628/