How to enjoy around Disney World without entry?

Spend a night or two at Fort Wilderness, the WDW campground. You get all the WDW guest privileges like use of transportation system and being able to visit hotels and restaurants throughout WDW. At Fort Wilderness there is a free petting zoo and the big horses along with a sandy lake shore and a pool area. Each resort has things to see and do for free and of course food offerings. Every evening enjoy the Fort Wilderness free outdoor movie and weenie roast with sing along. Maybe see a show. 

Enjoy WHAT 'around' there?

Do you mean to ask what else there is to do in the vicinity of WDW?

That depends what you like doing.  There are malls, other attractions, shops, etc.

You can visit Disney Springs without a ticket to Disney World - it has some shopping, dining, and entertainment.  You can also visit the public spaces of the resorts, some of which have some good places to eat and some fun things to get into.  But you can't, obviously, enter any part of the parks without an entry ticket.  While in Orlando, you may also want to check out the Universal CityWalk, which is the Universal version of Disney Springs.

If you don't enter, you can't be inside it. 

Perhaps you should take a look via Google Earth instead