Keep the IHG open. This one is a no brainer (unless you plan to churn it)

You can keep the Club Carlson open if you MS on it, value the Gold status (useless IMO) or think that 40k points are a good buy for $75. If not, you can downgrade to the no annual fee card and still have the last night free benefit available.

The Citi Aadvantage might be worth keeping for the 10% mile rebate if you max it out every year. Also if you travel AA/US enough to use the baggage/priority boarding benefits. If not, then downgrade it to the Bronze card which is no annual fee and will preserve your credit history.

The Marriott card is a difficult decision. Personally I do not value the Cat 5 cert at $75 due to devaluations over the last few years but you should evaluate this with your own travel plans. It has no other useful benefits that justify the fee. If you are not sure then close it and reapply for it 24 months after your first bonus.

PS: don't forget to fish for a retention offer on all the cards regardless of what you end up doing.