Close to the Impassable Greatbridge Site of Grace

You'll have to get to the Impassable Greatbridge in the far south to begin Elden Ring Runes. The most effective route isn't from your Site of Grace you unlocked in Caelid earlier, because it's far away and surrounded in enemies that will draw you in quickly. Instead, take the east route from Limgrave, and then south to follow the road through Caelid. You may also want to get the Caelid map and then unlock Sites of Grace while on your way.

Close to the Impassable Greatbridge Site of Grace is a war between giant demon dogs. They'll begin fighting as soon as you approach them, and after that, you'll be able to sit back and relax. I suggest sitting on the rocks next to the wall with the damage, because you'll be able to see the wall and stay out of danger.

The dogs will earn you less than 200 runes however, there are plenty of them. The dogs will yield 313. The soldiers always win the fight but you can prolong it by pulling on a few dogs who are close to the northern part of the battlefield. The goal is to collect between 2,000 and 3,000 runes, and with the Site of Grace right next to it, you can return to the fight in a matter of minutes.

Watch out for soldiers who sit on the tower next to you, as they will be shooting you with their crossbows. There's some loot on the high point, however it's possible to avoid them should you wish buy Elden Ring Items, as they will not be able to attack you if you're already past the massive fire, which you'll be if standing on the rock.