When are you travelling? (dates),,, Hotels prices will vary from day to day depending on events... and seasons...
Sorry - I would be travelling at the worst time - July long weekend.
Check Zero 1 based on this search on TA. You might have to find a lot to park... Your budget doesn't allow for parking...
If you want free parking, you might want to check in the suburb... like the Sandman in Longueuil. (metro a few steps away)Edited: 05 June 2018, 16:40
My apologies again. I meant that the hotel should have parking facility. Not that parking is included in the price.
Just to give you a sense of what you are facing, in late April I stayed at the Travelodge on Rene-Levesque, an okay budget hotel with rather small rooms, located on the southern edge of the Quartier Des Spectacles and a 10 minute walk to Old Montreal. I paid $120 a night, plus nearly 20% in taxes and fees. Their current price quote for the July 1 holiday weekend is about $230 a night, plus the taxes and fees.
Select a few hotels that you might like, keeping in mind that your budget is very low for this time of the year and then use trivago.ca to have price comparisons.