Node RED in the Cloud - langanjp/PI-NodeRED GitHub Wiki
IBM Bluemix
You can get free runtime from IBM to run Node-RED 24x7 in the cloud. As long as you use 512 MB of RAM or less, it is free (even multiple run-times - total memory must be 512 MB or less). It also includes a limited amount of Cloudant NoSQL to store your Node-RED configuration (and to use in Node-RED if desired). You can sign up for a totally free (no credit card required) to get you started for 30 days, and then continue on after 30 days with a credit card. (Note: the free 30 days gives you up to 1 gb RAM - but be sure you only use 512 MB or less!). See this link for details: http://nodered.org/docs/platforms/bluemix
Author's note: I have been using Bluemix for over a year and it has been very reliable (and free!). I use this to get information for my Wink Home Automation system and other feeds into my PI System.
SenseTechnic
You can get limited run time for free from https://fred.sensetecnic.com. They also offer 24x7 monthly plans starting at $9.99 a month with limited nodes.
AWS
Amazon's EC2 platform can be used for free for a year. See https://nodered.org/docs/platforms/aws for setup info.
Azure
See https://nodered.org/docs/platforms/azure to get started.