The only reasonable course of action would be for Aragorn to go to Lothlorien as he had. His destination inherent was to reach Mordor/Minas Tirith. There's no sense in going to Rohan. For one, it's the wrong way (away from Mordor). Two, it would bring the company closer to Saruman (I wouldn't want to be near him if I didn't have to be). And three, Aragorn had no knowledge that there was any bit of turmoil going on in Rohan. Aragorn found out about Rohan's situation from Eomer, when he arrived in Rohan. And in that exchange Aragorn says that it has been a while since he had ridden within Rohan, so he wouldn't have known of their situation first hand either.
The only other possible direction I can think of would be to go east to try and get in through the back door of Mordor on it's northeastern side. And while he might be able to muster help from Legolas' mates from the woodland realm, the trek east is more perilous than that down the Anduin.
~Scott
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Those who the Gods would destroy, They first make mad.
~Those Crazy Greeks
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