First, having location turned on shouldn't kill your battery. Having the various check-in settings turned on will, but letting your phone track it's location via cell towers costs nothing. It's got to constantly check its location anyway, otherwise it wouldn't receive any calls.
But the answer to your question is easy. Tap and hold the weather widget. Wait for the trash can icon to appear at the top of the screen, then drag the widget to the trash can. To add a new widget, tap and hold on a blank area of the screen. When the menu pops up, tap "Apps and Widgets." Select the Widget tab at the top of the screen, and scroll left or right until you find the widget you want. There are lots of them. Tap and hold the widget, and when your home screen appears let go. The widget may prompt you for some setup options.