A great way to get a feel for Manila is on the Pasig River Ferry. For about a dollar (50 Philippine pesos) one can enjoy about an hour tour from the water taxi.
Start at Guadelope station and ride to the final stop at Intramuros station. From there, one can explore the walled city.
The sights along the way are interesting. One will see what life is like for the people who inhabit near the banks of the river. In addition, one can see many of the tall buildings up close. The ferry also passes the presidential mansion (no photos allowed).