Ben, have you already come across the <em>kalyespeak.com</em> podcasts?

Tara lets!!

This is not a website but a mobile app.  I hope this app may help you learn Tagalog : https://play.google.com/store/apps/details?id=com.dalubhasareviewcenter.easytagalog

This app will teach you from different ways of counting in Tagalog, telling time, travel and dining phrases to advanced Tagalog. This app consists of Tagalog words and sentence structures and offline dictionary with example of sentences. It also has detailed explanation even on using affixes, verbs, adjectives, slang, Taglish, and idiomatic expressions and a lot more... Its free to download.

Peachey, thank you, I will check that out !

Koi, I do have already a few filipino language partners, it's just that, in your case,  I don't have much to offer in return!  But I might ask for additionnal help from you sometimes anyway...Thank you so much!

I don't know any Tagalog exercises website to help you but I could help you with Tagalog. 

Tagalog native here. :)