Go for Delhi sight seeing in HoHo bus or can try a metro to go to akshardham where you can spend a whole day and an evening in musical fountain but don't go on Monday as mostly all monuments are close on mondays. If you wanna spend your time in shopping than go to sarojini ngr market you will love that place and it is the best place on shoestring budget with lot of choices of clothing, household items & home decor items. Next day you can go for a sight seeing, as hotels where you stay can arrange a day tour on a bus & its gonna be very reasonable option too. Have a great time in Delhi.
Visit areas like Jama Masjid Old Delhi), Paharganj (Backpackers District), Sarojini Nagar (for shopping) and Lajpat Nagar.
You must opt for Ho-Ho bus, as they take you around the city at budget-friendly prices! For shopping you can visit Chandni Chowk, Majnu Ka Tila and even Janpath Market. And there many little cafes and restaurants in these areas that you can stop by for a hearty meal.