It's really a no-brainer! You have DirecTV....use it.
To get HD you need an open faced antenna either mounted on a tripod or a fully automatic roof mounted unit. Start out with the tripod and if you don't like spending 20-30 minutes at each new location getting setup you can spend about $1800 for a roof mount. Time and money are sometime interchangeable and you need to figure out which is more important to you.
If none of that sounds like any fun, you are still going to have a high expense if you want to go with Dish unless you want to also convert your house over to Dish. Paying for both services (even when it's only when you travel) makes no sense at all.