jQuery buttons to show/hide info and search
The first thing that comes to my mind is that what you're trying to do is handling all of the click events in just one handler function! Don't!

Use delegate event listeners instead:

$(document)
    .on("click", ".info-icon, .info-tab", function(e) {
       e.stopPropagation();
       // Deal with .info-icon or .info-tab
    })
    .on("click", ".search-icon, .search-tab", function(e) {
       e.stopPropagation();
       // Deal with .search-icon or .search-tab
    })
    .on("click", function(e) {
       // Other clicks
    });


Secondarily, define CSS classes list .info-tab-open and .search-tab-open like these:

.info-tab-open {
    max-height: 200px;
}


(And remember: using magic numbers is bad, especially when styling with JavaScript.)

So you'll end up doing this instead:

var $infoTab = $(".info-tab");
if ($infoTab.hasClass("info-tab-open")) {
    $infoTab.removeClass("info-tab-open");
} else {
    var $searchTab = $(".search-tab");
    if ($searchTab.hasClass("search-tab-open")) {
        $searchTab.removeClass("search-tab-open");
        setTimeout(..., 300);
    } else {
        $infoTab.addClass("info-tab-open");
    }
}


Third: since the handler's code is basically the same and repeating code is a code smell, you'll probably be better off if you use a factory function for the handler:

function toggler(selectedClass, otherClass) {
    return function(e) {
        e.stopPropagation();
        var $selectedTab = $("." + selectedClass);
        if ($selectedTab.hasClass(selectedClass + "-open")) {
            $selectedTab.removeClass(selectedClass + "-open");
        } else {
            var $otherTab = $("." + otherClass);
            if ($otherTab.hasClass(otherClass + "-open")) {
                $otherTab.removeClass(otherClass + "-open");
                setTimeout(..., 300);
            } else {
                $selectedTab.addClass(selectedClass + "-open");
            }
        }
    };
}

$(document)
    .on("click", ".info-icon, .info-tab", toggler("info-tab", "search-tab"))
    .on("click", ".search-icon, .search-tab", toggler("search-tab", "info-tab"))
    .on("click", function() {
        $(".info-tab").removeClass("info-tab-open");
        $(".search-tab").removeClass("search-tab-open");
    });