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The computer does not have to be present if you go overseas and install a new sim card.
One thing you might need to check with your current provider (if you purchased it subsedized) is to check and see if it is locked to their network. If not, you are free to use any card you wish. Just be aware that the iPad 2 uses a Micro-SIM so the carrier you choose would need to provide a Micro-SIM card.