Internet speed slow - router?

Not shocking to find upset customers here.

I find cox customer service to be severely lacking but I'm sure other do as well.

In any case, I recently started having trouble with slow speeds lots of buffering.  This started right after a cox 'outage'.  After the outage my internet didn't work at all... I called and was told to buy a new modem.  I did.  My internet now works but at slower speeds w/ buffering.  I called and was told either get a tech to come out or perhaps increase my speed... so I did that... I am now paying for 500mb... problem not solved plus I am getting only 160-180 when I do the speed test. 

my question is could the router be the problem?  Or is it just that cox can't provide the service they are charging me for.  There is nothing wrong with my wiring.  It was all fine before their 'outage'... also, my next door neighbor who has cox is having the same problem.

Should I replace my router or just get rid of cox?