Does this have a very strong wireless signal?

I would not recommend putting this unit in a closet because wireless signals can be affected by interference. I had interference issues that turned out to have a lot to do with my ISP that I initially believed were related to the router.Regarding the router itself I had to tweak the settings a bit ( mainly security settings and the channel) to find the best signal for my wife's laptop. ( Their customer service is very helpful as well)
I had to compromise a bit on the security settings , otherwise it would not allow Xbox live to connect. I also ultimately decided to hardwire the gaming console (via 100ft cat6 Ethernet cable) because it provided the most stable connection. Wired connection is outstanding as well as my wireless signal. If you want to run wireless with your gaming console, it is much easier to troubleshoot if you have a separate modem and router. I would not suggest a second wireless router because you will very likely encounter interference between the wireless signals. I had negative results trying to use range extenders. It seemed too troublesome to provision without the signal degrading or becoming very unstable. (most of the time BOTH unstable AND degraded signal) This particular router can cover a 200 foot radius.
I hope my reply was helpful and helps save you a lot of time and aggravation.