Just because you are on a budget doesn't mean that you can't be romantic. Being thoughtful and knowing what your lover likes is what it takes to make the perfect romantic outing, no matter the amount of your bank account. Doing something new or going to a place you both enjoy is a good way for you to share a romantic date.
Cook Dinner Together
Spend the night cooking dinner and dessert together. Choose recipes that are new to both of you and learn how to make them together. Choose a recipe that doesn't call for a lot of expensive ingredients, and pick something that uses things you already have in your home so you don't have to buy much. Serve it on your nice dishware so your date feels more like a night out.
Have a movie marathon together. Choose your favorite movies so you can each learn what the other person likes. Another option is to get a trilogy of movies, such as Star Wars or Lord of the Rings. Have lots of movie theater food as well, such as popcorn and candy. Since you want to save money, buy frozen pizzas or pasta at the store so you don't have to order out and can just stay in watching films and enjoying your time together.
A very cheap, very romantic date is to go stargazing. Drive out to a place where there are very few lights so you can see as many stars as possible. Set out a blanket and lay down together. Bring other blankets to cuddle up in if it is a chilly night. A star map allows you to find the different constellations. Make sure to look for shooting stars so you can make a wish.
Have a Picnic
Plan a picnic for the two of you. Find a grassy hill or a park near sunset so you can watch the sky turn colors together. Choose a place that is scenic but doesn't have too many people around, as this can take away from the romantic atmosphere. You can bring electric candles with you to set the mood for dessert after the sun has gone down.
Instead of spending the money to go to a spa, get some scented oil and give each other massages. The physical nature of giving a massage is romantic and intimate. After you give each other massages, you will be relaxed and can spend a nice evening together.