What advice would you give to a Canadian visiting America for the first time?
All these are true for every country.
Phone your bank(and/or visa/mastercard) and tell them you are travelling out of the country, when and where you are going, and for how long. Otherwise your accounts may get frozen when you make a purchase. Ask about travel insurance. They may provide it.
Buy travel insurance if not. Its cheap. No, its cheap, trust me.
Get immunization shots for the climate you are visiting.
No joking at the border. No small talk. No complaining. In customs for any country, you want to be the person that gets the least attention, so you get through quickly.
If you need directions or advice when in the US(in any country), rather than approaching people on the street(especially the police), ask at a tourist booth, a hotel, a restaurant, or other business. They are expecting to be approached by strangers and you'll get better reactions and results. Often they will have a map and a familiarity with the area.
Police are there to maintain civil order(or at least do their jobs), not necessarily help you out. These are not the same things. In some countries the police can be corrupt, and you do not want to interact with them or draw attention to yourself.
So don't speed while driving. Obey local laws.
Do not participate in political activism. If you get arrested you will be tossed out of the country(at least) and banned for life. Again, this is true of any country.
Keep identification on you at all times. Foreign law enforcement may not recognise your regional ID, so a passport is the best option. Keep a photocopy of your passport and extra money separate from your regular wallet and purse. Don't flash your cash. You can probably exchange large bills at your hotel front desk.
Don't put your wallet in your back pocket, and put your purse strap over your head. Don't valuables in a backpack that you are wearing on your back. A pickpocket will go through it and you will never notice.
You can wear a backpack on your front if need be.
Stay in well lit areas in the evening, and near groups.
A cheerful one: spend your change before coming home(or keep it as a souvenir). Banks won't generally change it for you. Either keep the larger denominations for the next visit, or change them back when you get home.
You MUST get medical insurance coverage every time you go to the USA. You can generally get a decent deal on it through your provincial automobile club.
Do not bother getting US dollars ahead of time. You get the best exchange rate by just using your debit card in a proper bank ATM to get US cash. Don't use convenience store or gas station ones unless the ATM is from a big bank. Airport ones are OK.
Realize both countries have great similarities. Depending on where you go, connect with the local populace, see popular sites. Canadá enjoys a favourable impression un Américan minds.