In Settings -> Main / Admin settings, there is an option to enter FTP details. Doing this will create a FTP link directly to your sy-upload folder (where you upload photos) in your admin header (upper right corner of the pages).
If you can set up your browser or FTP program to open when a FTP link, this will open your FTP program and take you directly to the sy-upload folder to upload photos.
If you are using Firefox for a browser, you can download the FireFTP add-on. Once you have it installed, open up the Options. Click on the Interface tab and check the checkbox for "Configure FTP links in Firefox to automatically use FireFTP.
You may be able to configure other FTP programs to open by default on FTP links in your brower.
Link to your FTP public folder
To get your FTP link, connect to your website with you FTP program. Go into your main public folder (like public_html, httpdocs, etc..) What ever folders you have to go into to get to your public folder is your FTP link that gets added to your domain.
Do not add www. or http or ftp to your domain for the FTP link.
cPanel servers (bluehost, bludomain, hostgator, saratoga hosting, and many more):
Your FTP link would be: your-domain.com/public_html
Hosting at godaddy, the main folder is the public folder so your FTP link would be your-domain.com