Robin’s Lost Axe is an early-game quest in Stardew Valley. You’ll receive a letter from Robin on the 11th day of Spring (1st year) asking you to find her lost axe in exchange for a reward. Here’s where it’s at.
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Where is Robin’s Lost Axe?
Robin’s lost axe can be found to the southeast of Marnie’s ranch, a bit north of the sewer’s entrance. However, you’ll need to accept the quest before the axe actually appears on the screen. Check your mail on the 11th day of Spring during the first year. You’ll have a letter from Robin saying:
MISSING:
I lost my favorite Axe! If you find it, please return ASAP. I’m having a tough time without it. There’s 250g in it for whoever finds the thing.
-Robin
At the bottom of the letter, you’ll see Accept Quest. Once you select it, the quest will begin.

Once you’ve accepted the quest, it’s time to find Robin’s axe. First, leave your farm from the southern exit.

You’ll now be at Marnie’s Ranch. Go down a bit until you’re in front of her shop.

From there, head south until you see two bridges connected to a small plot of land with a tree on it. Cross the bridges.

Finally, keep walking southeast, hugging the cliff to the right. You’ll eventually find Robin’s axe.

Select the axe to pick it up. You must have at least one free spot in your inventory to carry it.

Once you locate Robin’s axe, it’s time to bring it to Robin and claim your reward.
How to Claim the Reward for Finding Robin’s Axe
You have to return the axe to Robin before you can claim your reward. On most days, Robin is found working at her shop, located to the north of the town square, between 9:00 AM and 5:00 PM (4:00 PM on Friday). However, she’s off on Tuesday. It’s easier to catch her while she’s working since her schedule fluctuates during her off hours.
Once you find Robin, make sure you have the axe selected in your backpack. Your character will be carrying the axe over their head (like some sorta serial killer) when it’s selected.

With her axe in hand, talk to Robin. She’ll thank you for finding her axe.

After you give Robin her axe, you can claim your reward by opening your Journal and selecting Robin’s Lost Axe from the list.

Next, hover your cursor over the reward at the bottom of the journal entry and select it to claim it.

The money isn’t the only thing you get for finding Robin’s axe, though. In addition, you’ll also receive 1 Friendship heart, making Robin like you that much more.