The entire "unreasonableness" is based on the idea that this was Trump randomly banning countries.
Obama's administration (not Trump's) compiled the list of countries. It wasn't racial or "because they're Muslim" (most Muslims aren't banned).
What was the common thread between the countries? 6 out of the 7 countries have been on and off the US "State Sponsors of Terror" list for the past 40 years. Somalia (the one that hasn't been on the list) has spent most of the last 25 years in anarchy.
The law also explicitly gives the president the right to make the decision (see section f https://www.law.cornell.edu/uscode/text/8/1182).
In 1993, SCOTUS ruled that a much longer ban against the poor, non-terrorist, mostly black Haitian immigrants by Bush Sr. and Clinton was legal in an 8-1 ruling (http://www.nytimes.com/1993/06/22/us/the-supreme-court-high-...).
The constitutional claim doesn't hold water (foreign nationals have no right to travel in the US and the countries were selected for terrorist connections). That leaves only interpretation of the law, but the law clearly states POTUS has the authority. A 3 month break to find out what policies to put in place against 7 problematic and terrorist sponsoring countries is hardly something SCOTUS will find unreasonable.
EDIT: for the record, I think the bans are ineffective at stopping terrorists and are just Trump following through on his populist promises. That's different from the legality of the decision. This isn't the only thing Trump is doing While everyone has eyeballs here, they miss everything else that's happening in DC, and he still gets to look good when SCOTUS agrees with him.