Just install iTunes on your new computer. If you want to sync content from iPod to new computer via iTunes, you need to keep in mind that iTunes only lets you sync iTunes Store purchases
Step 1. Once you're on the new computer, install iTunes on it. Once installed, open iTunes, navigate to iTunes preferences (iTunes> Preferences on a Mac, or Edit> Preferences on Windows). Click the Devices button and make sure "Prevent iPods, iPhones, and iPads from syncing automatically" is checked.
Step 2. Now you are able to transfer all of your iTunes purchases (including free apps, paid apps, songs, books and movies) from your iPod to your new computer. To do this, right-click (CTRL-click on a Mac) your iPod within iTunes and choose Transfer Purchases. Or click "File > Devices > Transfer Purchases from my iPod". Then iTunes will start syncing the purchased items to the library.
After finishing the above steps, you have just successfully transferred all your purchased files from iPod to your new computer. So what about other non-purchased files? Like some nice music you ripped from CDs or some movies you got from DVDs. As is mentioned, you are only allowed to sync purchased items between iPod and computer with iTunes. When you restore your iPhone, the non-purchased items will be erased without any doubts. In order to sync all your data from iPod to new computer without any data loss during the transfer process, you can take advantage of the third-party iPod transfer software to solve the problem.
How to Sync iPod to New Computer