Yes, both "We took many rides" and "We went on many rides" are grammatically correct and commonly used, but there are subtle differences in usage:
"We took many rides": This phrase is acceptable and sounds slightly more formal or structured. It emphasizes the action of taking part in the rides.
"We went on many rides": This phrase is more casual and commonly used in everyday conversation. It emphasizes the experience of being on the rides.
Both are perfectly fine, but "went on many rides" might feel more natural in informal speech.