You need to think about your individual situation in order to answer this question. Some people are very comfortable with the idea of moving to a senior living place and they want to be part of the process. Other times you will have someone who is nervous or hesitant about it but they have to move for their own safety. You need to think about what is best for your family member.
I did not take my mom to look at first. I decided it was too overwhelming for her and I decided I would screen a list of places and then once I narrowed them down I would take her to see the final list. This worked out very well for her as she did not feel overwhelmed and I had been able to narrow things down to places I thought she would like and that had what she needed. They were also facilities I knew we could afford. It would be hard to go to a place that she loved but that we then found out we could not afford.
Also be prepared that you may need to take mom or dad back there a few different times. My mom kept not remembering exactly how each apartment size configuration was so we went back two or three times to look at them. One suggestion I would make is to take pictures of the rooms at the facilities so you have something to remind you of which facility had which types of rooms and which room number was which type of room. At the place my mom is now the studio apartments are all different. Each one is configured in a different manner, with different features and pricing.
You can also make sure that you have a short list from your loved one about what their must have features are so that you can make sure the places you like have those things. Anything you can weed out will help make the process easier. As I have said and will continue to say, this process is overwhelming and the best advice is to take it one step at a time.