Works perfectly for me. I have my PS4 hooked up via ethernet. I was able to play GTAV on my Vita in Los Angeles, connected to my PS4 in San Francisco and it was 100% solid.
Some tips:
1) Turn off power save mode on the Vita
Settings > Power Save Settings > 'Use Wi-Fi in Power Save Mode' should be off
2) If you can connect the PS4 up via ethernet, it's way better.
Frankly, this is the way to go even if you don't own a Vita. You'll get much much better download speeds on the PS4. Not wired for ethernet? You might want to consider ethernet over power solutions which work pretty well (eg.
http://www.netgear.com/home/products/networking/powerline/)
3) If you ever plan to connect via the Internet, you should forward the correct ports on your router.
http://faq.en.playstation.com/app/answers/detail/a_id/9539/~/ps4™-remote-play-and-second-screen
Recommended:
Minimum upload/download connection speeds of 5mbs down and 1mbs up for Remote Play via the Internet.
Port forwarding of TCP port 9295, and UDP ports 9296 and 9297. If these ports are unavailable, it might be possible to use ports 9295 through 9304 for both TCP and UDP.
4) If you want to connect wirelessly, you can choose to connect directly instead of through your router. There is a setting on the PS4 side for this to connect to the 'PS4 as Wireless Access Point'
5) Adjust the Video Quality - in the Remote Play app, you can set the Video Quality to 60fps if needed. Test at 30fps first, as 60 will be double the bandwidth.
6) You may want to run through the PS Now network troubleshooting steps. Running their network test may also give you an indication if the problem is on the PS4 side.
https://support.us.playstation.com/...bleshoot-Wired-or-Wireless-Network-Connection
7) Test from within the same room as the PS4 first, then move to other rooms. Wi-fi is pretty bad with dealing with walls or other sources of interference (microwave ovens, etc.) If you can't get it to work well in the same room, then try to figure out why. There are lots of ways wi-fi can go wrong.