A friend of mine got married at the registrar, then celebrated with friends and family that night at a nice restaurant for dinner.
She bought a semi casual white dress and had 2 bridesmaids. They did their own hair and make up, and their flowers were very simple.
They asked their guests for no presents, but for them to buy their own dinner.

They had a fantastic day. The most expensive thing for the day was the photographer, which didn't cost the earth either.

If you didn't want a restaurant setting, then you could have a celebration at the beach or in a backyard with caterers. Or you could find somewhere to have a ****tail reception.
It doesn't need to be expensive. You can either pay for meals, and guests buy their own drinks. Or guests buy their meals and you provide drinks.
Weddings can certainly be done on a budget. I wish I lived closer to you cause I love orgnanising weddings!