I can suggest for delhi - if you are looking for a budget stay then you can stay in hostel provided in hauz khaz village its right near the centre of delhi so you can easily commute anywhere you want to next if you are a non veg lover you should try the mughalai cuisine of purani delhi behind the jama masjid else if you are vegetarian then you can visit pandara road for a great dinner and if you are into clubbing you van visit connaught place you can find alot things to do ther. i hope it will help happy journey !