Charles Schwab is one of the best online brokers out there. They offer a wide range of low-cost index funds and ETFs, and this year dropped their trade commission fee to better compete with some new fintech companies.
Vanguard is a personal favorite of mine and is also a pioneer in index fund investing. Vanguard is the original and arguably the best place to buy index funds. It was founded by John Bogle, the man who created index funds himself.