I am looking for a device that has good support for being WiFi access point and being in client (managed) mode at the same time. Which can you recommend?

First let's get some basics out of the way.  I don't want to assume your knowledge level, so maybe you know this already (or maybe not).

 

Unless you have 2 sets of antennae on the device, won't this split your available bandwidth in half?  Assuming you meant client mode on the Wi-Fi as well, as this would essentially be a repeater.  Is it possible to wire Ethernet on one side?  If so, you could spare that loss.

 

I think some COTS router supported by OpenWrt might be cheapest (and/or perhaps even best).  But even that depends.  There have been some router discussions before around these forums, let me know if you have trouble finding them.  Some Armbian supported devices and some not.  Be aware that some devices had some flaky Wi-Fi interfaces (one in particular, it's escaping me at the moment, but that should be in the basic info page for the device).

Edited June 4, 20215 yr by TRS-80
add first paragraph