At the beginning of the game, Mayor Felix tells you his hopes for reviving their town bazaar with your help. Since you will be taken over the farm in the northern part of town, he expects you to sell your produced goods at the town bazaar in order to bring in more customers.
The world of Zephyr Town is, generally, just a series of horizontal areas with exits to the east and west side. Only your farm and the bazaar grounds are "north" of any main map screen:
The world is pretty straight forward; you live on Your Farm, most of the villagers live in Zephyr Town (with a few exceptions), and you sell your goods at the weekly Bazaar.
On Your Farm you will have a farm house, animal barn, and a field. If you want to unlock the other two outdoor fields, talk to Wilbur at the bazaar and order the expansions. The first field costs 30,000 G and the second costs 60,000 G. After that, he can build your basement greenhouse for 100,000 G. The farm area also has a Fermenting Windmill, which unlocks on or after Spring 23 of your first year.
In the Waterfall area you'll find Lloyd's and Emiko's house. Lloyd's is at the base of the waterfall, along the path, and Emiko is behind the waterfall. You can access Emiko's house after you reach your second year and exit Your Farm after 9:00 pm on a sunny or cloudy day. The Grinding Windmill is located here, which becomes available on or after Fall 20 of your first year. During Winter, the water will freeze, which allows you access to a little area of land in the northwest corner where you can find Snowballs and Ore Stones.
To the west of the Waterfall area is the Horse Track. Normally this area is blocked off by a large grouping of boulders that you can't destroy with your hammer. On or after Summer 2 of your second year, Felix and Enrique will reward you with a free horse. After that point, walk (not ride) to the blocked path to the horse track. At that point Wilbur and Felix will destroy the boulders for you. You can also meet Wada here, who somehow found himself catapulted here by unknown forces.
In the middle of the "world" you'll find Zephyr Town. Seventeen of the villagers live in this area, which contains a mixture of residential houses and two shops. This area is also where most of the seasonal festivals take place.
To the east of the main town is the Hotel Area. Angelo and Daisy live in this area, along with Amir when you unlock him starting Winter 1 of your first year. The long path that leads up the hill is for the Snowboard Contest in the Winter season and can be used for skateboarding during the rest of the year. The Manufacturing Windmill is by the Hotel, which unlocks starting on or after Summer 17 of your first year. Like the Waterfall area, this area has a Winter-only accessible section in the southeast corner.