You are doing all the right things (except your headline, which implies that you want one of 8 specific schools, when your post says you are looking more broadly at prestigious schools that are strong in your subject!).
As others are asking: is your goal academia or industry? are you looking for a Masters or PhD program?
If you are looking at a Master’s program, look at the program and faculty expertise to see the ones that are exciting to you, then look at where program grads tend to go- sector / industry / etc. It’s not a deal breaker, but it can help you target your application list, as well as tailor your app to the strengths of the program.
If you are looking at a PhD program, fit will matter even more: you will want to know the research focal areas well enough to have some rough ideas as to who you might want as your supervisor. Collegekid2 id’ed a couple of potential supervisors at each uni she applied to. She felt it helped shape her Research Statement, as she was able to link her experience to things that they were doing. For my PhD apps I pulled up the list of department research interests at the unis I was interested in, highlighted all the ones that I thought sounded interesting, and looked up the profs associated with each. At one uni, all but 2 were the same prof, so I went ahead and made an appointment- pre-application- to meet that prof. Talked about current research in the dept. Ended up being the only program I applied to- the fit was that good -and that prof became my supervisor.