I live in Sacramento, CA. Comcast is my ISP and I typically get results like this:

Pinging 204.2.229.10 with 32 bytes of data:
Reply from 204.2.229.10: bytes=32 time=26ms TTL=53
Reply from 204.2.229.10: bytes=32 time=26ms TTL=53
Reply from 204.2.229.10: bytes=32 time=28ms TTL=53
Reply from 204.2.229.10: bytes=32 time=27ms TTL=53

Ping statistics for 204.2.229.10:
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 26ms, Maximum = 28ms, Average = 26ms

However, at random intervals between 6pm and 11pm PDT, every night since patch 4.05 I get results like OP. Ping rockets up to 130-160ms and packet loss is rampant. I've traced the culprit to a chokepoint in Santa Clara, as you can see below:
Code:
Tracing route to 204.2.229.10 over a maximum of 30 hops

  1    <1 ms    <1 ms    <1 ms  CISCO35060 [192.168.1.1]
  2     9 ms     8 ms     8 ms  96.120.86.21
  3     9 ms     9 ms    10 ms  ae221-rur02.sacramento.ca.ccal.comcast.net [68.87.202.201]
  4    14 ms    13 ms    13 ms  ae-2-ar01.fresno.ca.ccal.comcast.net [68.85.120.201]
  5    21 ms    23 ms    20 ms  be-33667-cr02.losangeles.ca.ibone.comcast.net [68.86.93.37]
  6    20 ms    20 ms    20 ms  be-11599-pe01.losangeles.ca.ibone.comcast.net [68.86.84.194]
  7    21 ms    19 ms    20 ms  50.242.151.62
  8    25 ms    25 ms    26 ms  ae-19.r00.lsanca07.us.bb.gin.ntt.net [129.250.3.235]
  9   134 ms   122 ms   130 ms  ae-2.r23.lsanca07.us.bb.gin.ntt.net [129.250.3.237]
 10    23 ms    23 ms     *     ae-12.r22.snjsca04.us.bb.gin.ntt.net [129.250.4.150]
 11    27 ms    27 ms    27 ms  ae-19.r01.snjsca04.us.bb.gin.ntt.net [129.250.3.27]
 12    28 ms    27 ms    27 ms  ae-1.r00.scrmca02.us.bb.gin.ntt.net [129.250.7.31]
 13    27 ms    30 ms    28 ms  xe-0-1-0-1-1.r00.scrmca02.us.ce.gin.ntt.net [129.250.195.46]
 14    27 ms    27 ms    27 ms  204.2.229.234
 15    27 ms    26 ms    27 ms  204.2.229.10

Trace complete.
This "lsanca07" juncture reliably increases to 130ms+ whenever FFXIV suffers response delays. Does Square-Enix have any influence over NTT to compel an investigation?