Hamad International Airport (DOH) (مطار حمد الدولي)
Full of shops, modern, well functioning airport near city. Get there with taxi (affordable) or bus 777 which leaves every 20min and goes to Souq, MIA, corniche, pearl etc.
For local data SIM card, go to Ooredoo at arrivals (turn right after customs).
Al Mourjan Business Lounge
Huge and super impressive lounge by Qatar Airways. Normally only for business and first class passengers (one world emerald doesn't normally even get you in), but I think I got in due to morning rush hour...