The first time I used mySMS was so I could see, send and receive text messages on my laptop instead of my phone. The goal was to streamline my workflow and tune-out distractions.
Over the years mySMS has evolved into a very capable platform that's perfect for texting on an Android tablet. However, this isn't a self-contained app like Pulse and some of the others. Meaning you MUST have a phone in order to text on other devices. If you don't want to setup any weird accounts or create an entirely new phone number, just use mySMS Tablet. It essentially forwards everything to and from your phone -- to your tablet.
It's basically just giving you access to your phone messages (and incoming calls) on a tablet. This is great if you're phone is in another room charging, or you just use a tablet often. It's not a full-out system like some of the others, but that might be exactly what you're looking for.
mySMS Tablet connects to your phone and gives you access to all messages, and when you send a message it even goes through your phone. So the receiver doesn't notice anything different. Sync all of your messages and enjoy the beautiful tablet layout. Keep in mind that texting fees and charges still apply with this app, although you'll get unlimited messages if you text other mySMS users.