I would have lots of places, events and restaurants to recommend here but I would keep it simple first. This is especially if you only have a few nights stay.
This city used to be cheap (world class) but has now elevated its prices. Worry not, because it is still not as pricey as Japan or Korea. Manila caters to everyone. If history comes up in your mind, the Intramuros is a good visit. Find Spanish colonial time here. This is also where Jose Rizal, the national hero, was killed.
If shopping is what you look for, Manila is crazy with malls. The Mall of Asia would tire your legs with its vast indoor shopping stores and ocean view restaurants. Enjoy the sunset at this side of town. Greenbelt is recommended for a nicer shopping experience. they have boutiques from Bench to Louis Vuitton. The nicer restaurants are also found here. Landmark, Glorieta and SM Makati are all interconnected from this mall. Ayala Museum and Yuchengco Museum with nearby proximity are also nice to visit.
Marikina is a part of Manila where made to order and in stock shoes are famous. Imelda Marcos shoe collection is not found here but is still worth a visit. Last but not the least, do not forget to try Filipino dishes like adobo, sinigang, menudo at Filipino specialty restaurants. Halo-halo is also very good dessert.