Weird that I would just stumble on this. Yes, I do. Lots.
But I have no idea how much you want to spend on rent, or what you like to eat.
Good starts for food:
http://www.restaurantthing.com/
http://www.ottawafoodies.com/
Apartments, downtown: Metcalfe Street is right downtown and heavy on nice buildings. Ditto Cartier Street.
The 2nd bath is not all that common, and something like that will be expensive. Do you want a newish highrise, or a 'heritage' building?
Ottawa CL is worth a look:
http://ottawa.craigslist.org/apa/
This
http://ottawa.craigslist.org/apa/242678054.html
is cheap and big and in a nice, downtown-adjacent location. Almost suspiciously cheap, actually.
And, here:
http://ottawa.kijiji.ca/f-housing-apartments-for-rent-W0QQCatIdZ37
From the 'Ottawa Citizen' newspaper:
http://ottawa.renting.canada.com/properties/search/searchForm.php
Walking around downtown is, for better or for worse, one of the better ways to find a place downtown here at the moment.
Neighbourhoods you might want to check out:
http://en.wikipedia.org/wiki/Downtown_Ottawa
(note map w/street names)
http://en.wikipedia.org/wiki/Byward_Market -- loads of info on-line about it. A bit overpriced at the moment, though, and some areas are very seedy.
http://en.wikipedia.org/wiki/Centretown -- also prone to seediness in parts, but this varies wildly and can change a lot by a matter of just a few blocks.
http://en.wikipedia.org/wiki/Centretown_West -- as per Centretown.
http://en.wikipedia.org/wiki/Embassy_Row_%28Ottawa%29 -- nice, but possibly too far.
http://en.wikipedia.org/wiki/The_Glebe -- very nice older neighbourhood; great main street through it with a good mix of apartments and houses. Possibly pricey, but possibly worth it.
http://en.wikipedia.org/wiki/Westboro_%28Ottawa%29 -- as per the Glebe.
http://en.wikipedia.org/wiki/Sandy_Hill -- University of Ottawa neighbourhood. Combination of businesses, students, mansions; very mixed-use. Nice.
Feel free to e-mail me with questions. (NB: you are moving here with...is it a 10th-grader? Hardly anybody says 'sophomore' here...)
Edited to add: those buildings on Lees mentioned below are a bit slummy these days.