Talking about running (jogging)

[upthera44.livejournal.com]

One lingering question I've had in speaking Russian is how to talk about jogging. 

My friend and I go jogging and in the course of our run we might say things like: 

1. "Let's run to the bridge." 

Or afterwards we might describe our 'marshrut' and say things like

2. "First we ran to the trail by the river, then to downtown and came back." 

Do Russians use the word "bezhit'" plus prefixes when discussing these things? Or just "idti"? 

So is "Пойдем на мост" или "побежим на мост" или "добежим до моста" better for the first example?

And for the second example: 

"В начале ( побежали на / добежали до / пошли на ) набережное, потом в центр и вернулись домой."

Thanks for the help.