Is there a radius inside of which objects are (doppler) blue shifted?
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.