On our second date, my wife and I went to a bookstore and browsed together while having coffee, which naturally brought up shared interests and opportunities for conversation.
In addition to being relatively low-cost, these types of dates also have the added advantage of being easy to end naturally and without the, potentially awkward, requirement of waiting for a check.
Even if you find out you are not compatible, at least you will have spent the time doing something you enjoy.
Walks on the beach (or in the park) make for a great first date and provide opportunities for unscripted interactions and conversations.
A large financial investment into the first date may get a second, but when it comes to determining long-term compatibility, simply having coffee or going for a walk is likely to be as, or more effective than a fancy dinner.