One day trip to darjelling

I’ll be landing in Bagdogra around 12 PM and need to spend a day in Darjeeling before heading back to Bagdogra Airport by 2 PM the next day for another private tour. Looking for budget-friendly travel advice: 1.Transport & Budget Travel: Best budget-friendly way to reach Darjeeling and return? Shared taxis, buses, or rentals? Time taken? 2.Stay Options: Where should I stay? Budget hotels or homestays? Best websites to book? 3.Places to Visit & Eat: Must-visit spots in Darjeeling within a day? Best local food places (vegetarian options preferred)? 4.Return Timing: What time should I leave Darjeeling to reach Bagdogra before 2 PM? 5.Alternative Plans: Is Darjeeling feasible for this trip, or should I consider staying in Siliguri, Mirik, or any other nearby place? Would love your recommendations. Thanks!