Schedule routine phone calls.
Go on FaceTime dates.
Plan a Skype sleepover.

Watch a Netflix show together.

A thousand miles seems pretty far, but they've got planes and trains and cars and Skype and FaceTime and cell phones and other amazing tools to help keep the romance alive from across state lines.
Whether it's before and after work, on your lunch break or every night right before you go to sleep, figure out a system that works for you two and stick to it. Communication is the basis of any relationship and is absolutely essential to maintaining a LDR.
Different time zones doesn't mean dates are out of the question. Pick up a bottle of wine, order your favorite takeout, pamper yourself more than usual, dial your partner up on FaceTime and make a night of it - just like you would if you were together (almost).
The lack of physical touch is one of the hardest things about being away from your significant other. So if it's late night cuddles and waking up next to your loved one that you're missing, plan a Skype sleepover. Simply prop your computer on your nightstand and leave the application running all night. (You can even hit mute if your partner is a snorer!)
Couples committing to a Netflix series together has become the norm. Plan some time each week to dedicate to "your show," watch it at the same time and talk about it throughout and afterwards. Just make sure to abide by the golden rule: thou shalt not skip ahead unless agreed upon by both partners.
Whether it's rock climbing, running, or remote control car racing, pick something that you're both interested in and do it. Since you're not in the same city, you won't have to worry about working around each other's schedules to attend classes or reserve tee times, but you'll both be working towards a goal together. It will give you something to continuously talk about and you'll feel great about taking on a new challenge!
Send flowers or pizzas, postcards or little love notes as a reminder that you're thinking of your partner under circumstances that make it a little more difficult to show you care. Going the extra mile will make the extra miles between the two of you totally worth it.