Some "other" device/software/app, will determine "Wireless play of photos from device(Tablet) to TV". "THE" tablet may have little to do with it?
My thoughts for you are these:
ALL(Recent Model) Panasonic TV's(Other brands?), all by themselves, can play a slideshow or digital video, from an SD card or USB Flash/Thumb drive. No anything else needed. The TV remote even controls the slideshow/video. Maybe just buy a new TV? The Panasonic Plasma's are the longest lasting, best picture TV's in the world - perfect for viewing photos(Yes, I sold them last Christmas, FOR Panasonic - HA! So check out the pro reviews, yourself. You'll find it's true.).
Practically speaking: Almost all TV's(Including ANY older than, say... next year?) will likely need some sort of gadget, or propietary software/parts, etc.,(Which may not work with "your stuff") to do anything at all of this type, "wirelessly". Thus: "What TV, with what else?" has to be a primary question. Assuming Dad has a brand new "wireless capable" TV, along with whatever options are needed to make it work, few TV's Dad will encounter while visiting others, are "ready" to do anything wirelessly, without some sort of "device" to attach to it - which he would have to take along, attach(If there is an attachment point?), figure out how to make it work, etc. MOST TV's "out there", still have no "EASY" attachment points at all, for such things. Even those that do, still have "proprietary systems" that demand "all Samsung stuff - camera/tablet/TV", or whatever.
1. WHY we want tablets, in the first place, is so we can show people "our stuff", while sitting around the kitchen table, without needing anything else - period! Even the camera ON my "old" Samsung Galaxy 10.1 is pretty good! "The bigger the screen the better?". If desired, the Samsung Galaxy 10.1, can use it's "optional" HDMI adapter to hook-up to a newer TV(But it's not wireless.), or even the "ancient/optional" RCA plug TV cable! I believe Samsung offers wireless options, but..? I don't know enough about them. Confusing and "inconclusive" when I was trying to sell them(Yes, I sold the Samsung tablets, when they came out, too - ha!). Not ready for prime time, at that time(A year or so ago.)
2. What Camera? What does it use for "storage" and transfer of photos? There are Wi-fi capable cameras, today, which may "play" direct-to-TV - but careful investigation will be needed to determine if THIS camera will do THIS or only THAT. Again - if you are going to have to remove the SD card from the camera, or make-up a thumb drive, anyway, using a computer, why not just plug it into the TV and be done with it? It will be "wireless", fas as it goes.....?
2a. Sadly, IT IS NOT RECOMMENDED that you "mess with" the SD card IN your camera/device! When you buy the camera, pick the SD card you want, plug it into the camera and leave it there until the camera is replaced. SD-type cards were never designed or built for(Even moderate) "plug/unplug" from devices! One of the persons who designed/built/maintained the machines that made the gold contacts on YOUR SD card told me that. "Not enough gold. Sooner or later it wears off and the card is 'done'". I know "everybody does it", but, yes, a million people(And lots more!) can be wrong - and in this case, are.
3. So. To physically, conveniently carry/transfer, computer files, what one wants, these days, is a USB/Thumb Drive. Few cameras use them. Most TV's do not use them.
I've got to get to work, so, I'll make this quick:
What you want is "cloud storage", for ANY computer device - and a Wi-fi connection - maybe get Dad a BIG screen smart phone(Samsung Note? It is amazing! Truly spectacular - and it's own photos and it's own screen are georgous! And he can pass it around like passing around a pile of snapshots in days of old.). Add a "hotspot" to it, so he's never without Wi-fi - another stunningly important "invention" which, along with cloud storage, helps alot to seal the "use the computer for everything" deal.)...... Then, when you want "it"(Photos/files, whatever), it's "right there", for any Wi-fi capable device with anything remotely like a "browser"(Including that new, big screen, "smart" TV!). This negates the need for "mass storage" on ANY device, as well as most "physical connections" of devices. Still, "convenience" is the least of "the cloud" qualities. Security is light years better than anything we've ever had(Security against loss or device breakage. For "family photos", privacy is not necessary - I hope! Though, it can be pretty darned good, as well.), and again, wherever you are, there it is! Hard to beat. "Pull-down" folder #14, on whatever device you have, show it to the folks, then just "dump it" from the device(Camera, tablet, phone, laptop, TV, whatever.) when you're done.
"What tablet" may be the least of the questions, in this case(I don't believe my old SSG10.1 has been beat, yet?) - as Stiltskin says, most are "fine", far as it goes. As usual, when buying anything - get the one with the latest operating system, the fastest processor, the most RAM, the most storage, the biggest/best screen and the lightest weight you can afford and be done with it. Keeping in mind that some of the $250, 7", machines(Nexus/Samsung "2") would be "very fine" most likely. If it MUST be "wireless", tablet to TV, what software and devices are needed to do the "wireless part" and which will work with THIS tablet, are prime questions.
As much as what we read may try to tell us that "all your stuff everywhere on any device anywhere" is "here today!", it is not - quite. Anything you buy, today, must still be considered "BETA"(All of this is in it's infancy.), and subject to re-purchase next Christmas - from camera to "interface gadgets/softwear" to computer device to TV.
Live not thee in the past, but never too far into the future......
Happy Honda Days!