The online only "high yield savings accounts" pay much better than a regular bank account. Read reviews and pick one with FDIC insurance (and may that's been around a while?) Discoverbank, Ally.com, Marcus are all big players. Ally has a nice "Buckets" feature where you can sort out what the money is "for."

Open the account and link it to your existing checking account to move money back and forth. Remember that transfer take a few days so plan ahead to keep enough money in your checking account.