I was wondering if excluding airfare $2700 American would be enough to get by somewhat comfortably visiting Paris, Barcelona, and Amsterdam for three total weeks. I had planned on visiting mostly museums, eating fairly good food, and sleeping indoors. I am traveling alone but the prices I have been reading online make it seem like eating alone is quite expensive in the areas I plan to visit. Any advice or comments are appreciated.
I'm afraid I don't understand USD, but a lot depends on your definition of "fairly good food". A nice Parisian restaurant will easily set you back 50-60€ for two courses and a glass of wine, a set meal in a more modest restaurant (like the Relais de l'Entrecote chain) will be in the region of 24-26€, plus 9-10€ for a half bottle of wine or 3-4€ for a glass, a nice breakfast with coffee, croissants, jam, butter etc. will be 15€, a coffee or hot chocolate in one of the popular cafes (Cafe de Flore etc.) will be 5-7€. You'll pay less at the smaller, local cafes and restaurants.
The cost of accommodation varies depending on location, time of year, how far in advance you book and how nice you like your room. I'd budget for a minimum of 100€ per night for something basic but decent, up to 250€ for a 4*.
Prices in Amsterdam and Barcelona will be fairly similar. Make sure you've budgeted for travel between the three cities.
If you hostel and eat in cheaper small local cafes you'll be fine on that budget. If you want hotels and restaurant food you need to at least double it.
I agree with Sallyxx - it depends on what do you mean by saying fairly good food and sleeping indoors. If you wanna stay in a youth hostel or a low budget hotel yeah that's enough, but if you're planning on sleeping in a fancy 4* hotel then you should be prepared to spend more. You also have to remember about the cost of bus/underground/trains fares ecc.