Search engines know a surprising amount about us. I'm so-so on them. If I want hyper-local searches then I use Google, just because it excels at that, and I don't have to type in all the localized terms like city and state just to get decent results - Google figures that out by itself. Other than that, I try to avoid using Google because of privacy reasons. That said, non-Google doesn't automatically mean private. Bing uses personal data also. I have recently been using DuckDuckGo as my default search engine, which has actually been very helpful. That one is actually privacy-oriented. A few other things I do is (when I remember):
Use different search engines on different occasions - that way no single search engine knows everything I'm searching for. They only have a fragment of the picture.
Occasionally use a random search to add in an additional search here and there that is randomized. This makes it harder for the search engine to 'pigeonhole' me and my interests.
I also disable localization on my phone and also if I'm using a browser on my computer. If a web pages asks me to share my location, I refuse. For shopping online, if I need to see if something is in stock at my local store, or to see if there even is a local store near me, I'm able to do that by typing in the zip code (or a different zip code near me if I'm feeling really paranoid!) and it'll come up with which are the closest stores to that zip code. There is no need to use localization data for anything, unless of course I've gotten lost and need to have the phone navigate me back. That rarely happens though, and even then it's just a matter of turning on localization and turning it off after.
Overall, there are some privacy steps I have been taking.