You need to the water to circulate if you want 'instant' hot water. If you can afford to wait, and request it, you don't need to run the pump constantly. There are ways to activate the pump from multiple locations, if that's an issue.
If your piping layout will support it, it is possible gravity convection will keep the water warm (not hot, especially over 120-feet!). This would require a dedicated return line and a check valve back to the WH.
IF, and this can be a big if, you can get power underneath the sink in the furthest location, you could install what I have - a RedyTemp unit in about 10-minutes for a typical install. It is a self-contained pump, cross-over, check valve system. It's on the higher end, but it is really easy to install. I have one, and it has been working fine for pushing 8-years now with no maintenance. I have it on a timer, so it doesn't run while I'm typically sleeping, but it is fairly easy to setup to work via remote, or to bypass the timer entirely.
All systems require a cross-over, and you may need or want more than one. The more typical units have the pump back by the WH, since there's room and typically power nearby. Then, they put a cross-over at the needed sink(s). If you don't have dedicated return line(s), and you use a pump, it uses the cold water line as the return via the cross-over/check-valve. This means that when the valve is open, the cold water will end up warm until the aquastat in the cross-over closes the valve (and for awhile as it cools). The RedyTemp unit has a user adjustable cutoff point. I have mine set to have warm water at the sink...my shower is closer to the supply, so gets nearly instant hot. And, flushing the low-flow toilet pretty much clears the warm water from the cold line since I have it set to only get warm to the sink instantly (hot isn't far behind, though).
To make a gravity convection system work, the lines have to be sloped properly with no jogs (at least no upwards excursions) in the return line, or that will stop the convection. This can be hard to do, especially over 120-feet as you also need to slope it for best results. Without a temperature gradiant, there's no density difference, thus, no convection - just conduction, cooling the pipe off along with the water.
Personally, I think you'll find it really hard to get a convection, pump-less system to work over 120-feet from the supply to the point of use.