What's an easy approach to provide Wi-Fi/Webserver to mobile phone apps without hotspot
Why not try the TI wifi module, the CC3200, it supports ap mode so your phone could connect and has embedded stack. I think it's a slow arm on the inside. It wasn't too hard to add a simple http server to send commands and get feedback on the MSP430 so this should have more than enough power to do it.

It looks like the eval board comes with an HTTP server already in flash among other things.  I looked at their downloadable SDK and it lists "http server" as one of the examples.

Here's their eval board: the CC3200-LAUNCHXL



Good luck with the project!