No idea of your age, location, or preferences so here's the take from an outdoors couple. "Inexpensive" usually means an outdoor activity for us:
*Moderate - Sailing lesson and a picnic = ~$125.00. If you're near a lake, it's a unique experience for most folks and makes for lots of laughs and great pictures.
*Moderate - Canoe and a picnic = ~75.00. If you're near a navigable river, canoeing requires fewer skills than sailing. You might not even need the lesson--especially if the river is fairly shallow.
*Frugal - Day-hike and a picnic = ~$25.00. If you're near the mountains, it's fun. Plan for less walking and more relaxing. Areas away from the common tourist spots are the best. It's an anniversary after all.
Yeah, we picnic a lot too.
If your anniversary always includes an overnight stay, you will always be forking over funds for lodging which will always keep your costs a bit higher than a day trip. We prioritize our vacation/travel plans annually and usually celebrate our anniversary within a couple hours' drive from home or less. We travel further and spend for lodging at other times in the year.