I mostly lurk around here but I thought I'd chime in, given my experiences in these cities.
First, I'll have to side with Flaming C here. Apply for jobs in all three cities and move to wherever you find decent work (i.e. a job that you would enjoy and that pays well enough to live in that city). Finding a good first job following graduation can be difficult. Hedge your bets.
I would also suggest getting a Masters in Public Administration (MPA) if you want a good policy job in the public service or an NGO - a bachelor's degree in PoliSci isn't worth as much now as it used to, I'm afraid.
Now, if you have the leisure to choose, here is what I think is the bottom line on all three cities.
Vancouver
Pros: Beautifully situated city with temperate climate, amazing scenery and nature, beaches, great food (especially if you like seafood and Asian cuisine), laid back vibe, close to the US West coast and Asia.
Cons: Very expensive, lower wages than in Ontario, fewer NGO or government jobs, lots of rain, the city itself isn't particularly vibrant (compared to Montréal or Toronto), far from Europe.
Overall Vancouver is an amazing city, very unique in Canada, but very expensive. Choose Vancouver if you're into the outdoors and want a laid-back lifestyle but expect a much smaller disposable income.
Toronto
Pros: Large vibrant city with a very diverse population, great food, many job opportunities, good wages, excellent arts scene and overall a great city for an urban lifestyle (restaurants, bars, festivals, etc.).
Cons: Not the prettiest city in the world, can be expensive, perhaps more stressful than Ottawa or Vancouver, can feel a bit soulless at times (I keep comparing to Montréal).
Toronto is the undisputed commercial centre of the country, with great opportunities and countless things to do. Of your three choices, it is the best city to lead an urban lifestyle (I would argue that Montréal is even better in this respect). Choose Toronto if you want to live in a large city with good jobs, good pay, but don't expect it to look good.
Ottawa
Pros: "Pretty" city, many NGO and government jobs with good wages, less expensive than Toronto or Vancouver, very "livable" city (beautiful neighbourhoods, parks and nature right next door), somewhat bilingual atmosphere, good activities because it's the capital (exhibits, orchestra, concerts, festivals), close to Montréal, Toronto, NYC and Boston, really friendly population.
Cons: Smaller than Toronto and Vancouver (i.e. fewer restaurants, bars, etc.), more conventional population (school then marriage then house then kids then...), very cold in the winter, can get boring.
Ottawa is more easily compared to mid-size cities like Calgary or Québec City (I prefer Ottawa). It is smaller and feels less like a "big city" than Toronto or even Vancouver, but still boasts plenty of activities (the restaurant scene is booming, arts scene is good). It is a very stable, relatively quiet city with good, safe, and well-paying jobs; this is overall a good thing, but it may also appear boring to some. Choose Ottawa if you want to work for the federal public service and live in a relatively inexpensive mid-size city. Travel to Montréal if you really need to party.
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About French. Many, many positions in the public service are "English essential" positions and do not require French. I know countless unilingual anglophones with great jobs in the public service. Similarly, many, many positions are "Bilingual essential"; it depends on the line of work. Still, if you wish to move up in the ranks one day (I'm thinking manager or executive), being bilingual is not only an asset but a requirement. Luckily, the Government often pays for French (or English) training, and is fairly lax in its definition of "bilingual" (I know many "bilingual" managers with, in my opinion, a poor command of the French language). Most government work in Ottawa is carried out in English unless all people involved are francophones.
Long post, hope it helps!