I had the same problem - update couldn't be found for 10.10.4 and the update check kept spinning. I'm not sure the machine type matters as I'm using a late 2014 Mac Mini.
I did an update earlier on an early 2015 13" Retina MacBook Pro without any problems. However, it was previous to the bundling of the OS with iTunes. I updated the OS, and then later in the day iTunes 12.2 was available and I updated it.
The only suggested file I found to delete '/Library/Preferences/com.apple.SoftwareUpdate.plist' which I deleted and then restarted the machine. It found the 10.10.4 update (containing iTunes 12.2) in the Mac App Store which I was able to apply. The plist file I removed did contain the following which shows a reference to iTunes 12.2 which was not in the list of available apps to update:
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<dict>
<key>LastAttemptSystemVersion</key>
<string>10.10.3 (14D136)</string>
<key>LastBackgroundCCDSuccessfulDate</key>
<date>2015-06-30T20:26:20Z</date>
<key>LastBackgroundSuccessfulDate</key>
<date>2015-06-30T20:26:20Z</date>
<key>LastFullSuccessfulDate</key>
<date>2015-06-30T20:26:05Z</date>
<key>LastRecommendedUpdatesAvailable</key>
<integer>1</integer>
<key>LastResultCode</key>
<integer>0</integer>
<key>LastSessionSuccessful</key>
<true/>
<key>LastSuccessfulDate</key>
<date>2015-07-01T05:51:21Z</date>
<key>LastUpdatesAvailable</key>
<integer>1</integer>
<key>PrimaryLanguages</key>
<array>
<string>en</string>
</array>
<key>RecommendedUpdates</key>
<array>
<dict>
<key>Display Name</key>
<string>iTunes</string>
<key>Display Version</key>
<string>12.2</string>
<key>Identifier</key>
<string>iTunesXPatch</string>
<key>Product Key</key>
<string>zzzz031-13738</string>
</dict>
</array>
<key>SkipLocalCDN</key>
<false/>
</dict>
</plist>