As soon as you specify FDIC you immediately eliminate what most people would call investing. The word you use in the title "Parking" is really appropriate. You want to preserve the value. Therefore bank or credit union deposits into either a high yield account or a Certificate of Deposit are the way to go. Because you are not planning on a lot of transactions you should also look at some of the online only banks, of course only those with FDIC coverage.
The money may need to be available over the next 2-5 years to cover college tuition
If needing it for college tuition is a high probability you could consider putting some of the money in your state's 529 plan. Many states give you a tax deduction for contributions. You need to check how much is the maximum you can contribute in a year. There may be a maximum for your state. Also gift tax provisions have to be considered. You will also want to understand what is the amount you will need to cover tuition and other eligible expenses. There is a big difference between living at home and going to a state school, and going out of state.
The good news is that if you have gains and you use the money for permissible expenses, the gains are tax free. Most states have a plan that becomes more conservative as the child gets closer to college, therefore the chance of losses will be low. The plan is trying to avoid having a large drop in value just a the kid hits their late teens, exactly what you are looking for.
There are some high-yield savings accounts out there that might get you close to 1 percent. Shorter term CDs might also serve you well here- rates are above 1 percent, even with 1-2 year terms: http://www.nerdwallet.com/rates/cds/best-cd-rates/
Your objectives are contradictory and/or not possible. Eliminating the non-taxable objective:You could divide the $100K in 5 increments, making a "CD ladder"$25K in 3mo CD (or savings a/c)$25K in 6 mo CD$25K in 9mo CD$25K in 1 yr CDor similar structure (6mo also works well)Every maturing CD you are able to access cash and/or invest in another longest maturity CD, and earn a higher rate of interest. This plan also works well to plan for future interest rates hikes. If you are forced to access (sell CD's) ALL the $$$ at any time, you will only lose accrued interest, none of the principal. All FDIC guaranteed.If non-taxable is the highest priority, "invest" in a tax-free money market fund....see Vanguard Funds. You will not have FDIC guarantee.