Is there a radius inside of which objects are (doppler) blue shifted? The Andromeda galaxy is about 600,000 light years away and is doppler blue-shifted.  Are there objects closer to us than Andromeda which are red-shifted?  Are there objects farther than Andromeda that are blue-shifted?

I'm curious as to whether there is a more or less uniform radius from earth outside of which objects are generally all moving away from us, and inside of which objects are generally all moving towards us.
No, there is no spherical volume of space within which objects all tend to approach us and thereby show blue-shift. The fact that the Andromeda galaxy is blue-shifted is because at these relatively small distances the cosmological red-shift is much smaller than further away. Andromeda's own (non-cosmological speed) is larger then the cosmological speed away from us and it happens to move towards us and is therefore blue-shifted. It could also have been moving away from us, and be red-shifted as a result, but that red-shift would not be cosmological. 

I'd expect that the chance that a nearby (Local Group) galaxy is either moving away from us or moving towards us is 50%. 

Furthermore, the Andromeda galaxy, and all other galaxies belonging to the Local Group, are gravitationally bound and would therefore not show any cosmological red-shift anyhow.

NB. The Andromeda Galaxy is actually 2.5 million light years away from us.