Your first option is your neighboring public school. However, aside from the nearest public school, there are specialist public schools, as well as private schools. You can also do homeschooling.
Specialist public schools are funded by the government, but they may have a different curriculum from mainstream schools. For example, science schools focus on the sciences, while "comprehensive" schools offer a higher-level vocational training program than those offered in mainstream public schools. Most specialist schools require an entrance examination for their students.
Private schools do not depend on the government for their budget, although some of them rely on financial extension from the government. Private schools are required to follow the minimum curriculum set by the Department of Education, but they may add other subjects to the curriculum, for example, Christian Living. See below for a comparison between public and private schools.
Homeschooling is also an option. Although not widely popular in the Philippines, it is available for those who would like to take advantage of it. All you need to do is to register to a certified program. Take note though that this is quite expensive.
Public vs private schools
Public schools cannot charge tuition since they are funded by the government. Private schools, on the other hand, must source out their operating expenses from the parents.
There are expensive and not-so-expensive private schools though. Tuition can range from as low as PHP 200/month in some rural town to PHP 10,000/month in some exclusive school in the city. Generally, the more expensive the school the better its performance would be, although there should a lot of exceptions to this.
Private schools could also impose their own admission standards, and parents could not force a private school to enroll their child.
Generally, private schools perform better than private schools, simply because they have less students per teacher.
In most localities, the only private schools operating are those run by religious corporations, although this is rapidly changing.