If you are alone , you can visit anyplace you want.. because you don't have to be dependent on someone else.. But Yes, lajpat nagar market is nice.. you can roam in the market.
Bro you can start your day with AMA Cafe at Majnu ka tila and then go for a drive and visit Leopard trials and after that you can go to World mark, Gurgaon and then maybe drive back to your house.