The Weapon Connoisseur
Requirements
Nebb is available running around the middle of town roughly between noon and 7 pm. After you have started the quest, when you need to find him again, you can set this quest as the active one in the Adventure Log.
Walkthrough
Talk to Nebb to start the quest.
Tip: If you have done the Sunshroom Sensing Side Quest and have Sensor+, you can talk to Symin at the Hateno Ancient Tech Lab and purchase equipment pictures for your compendium (at 100 rupees each, getting a random picture each time, can buy in bulk if desired) until you have a picture for your next objective. You can then set it as your Sensor+ target for help in finding one.
Objective 1: Traveler's Sword
If you happen to have one already on you, you're lucky, just show it to him. It doesn't need to be equipped. Otherwise one can be found on the path just east of Inogo Bridge. He will give you a red rupee.
Objective 2: Fire Rod
To be continued...