One of the "smartest" features of an iPhone and Android phone is the capability to pull up as search suggestions previously visited URLs when you begin typing your destination into the browser.
If you're signed in to Google and you've also enabled search history in the Settings (Settings > Search History > Save Searches), then tapping the new History link that's sandwiched between your username and the "Sign out" link will produce a list of your previously visited URLs.
The Starred Items tab also gives you quick access to a list of places you've starred from either your smartphone or from the desktop. A thumbnail image of a map is icing on the cake.
The caveat is that History will only save those searches you did while signed in--it won't be able to capture URLs you visited as an anonymous surfer.
You can remove old history items by pressing an "Edit" button while you're reviewing your cache, and then deleting those unwanted records one by one.