Yes, of course. However, you need to be mindful of the tense used in the original question.
For instance, if someone asks, "What do you do on the weekends?", you cannot respond with "Walking in the park near my office." This is because "Walking in the park near my office." is actually short for "I'm walking in the park near my office." so you are using the incorrect tense. To be grammatically correct and to make sense, you have to respond with "Walk in the park near my office." which is short for "I walk in the park near my office." If someone asks, "What are you doing right now?", then you can respond with "Walking in the park near my office."
Also note that you need to be mindful of the person and number involved in the original question. If someone asks, "What does he do on the weekends?", then you have to actually respond with "Walks in the park near his office.", not "Walk in the park near his office." This is because "walks" is the correct verb conjugation to use with the subject "he". Likewise, you would have to say "Goes out to a club with friends." if someone asks you, "What does she do every Friday night?"