In the 80's and 90's one product that was popular was TV/VCR combo - which later morphed into the both the TV/VCR/DVD and TV/DVD combo. However, nowadays combo TVs are getting a lot harder to find, but they are not totally gone.
One example of a TV/DVD combo TV that is available, and worth considering, is the RCA LED42C45RQD. This unit features a large 42-inch LED-backlit LCD screen in combination with a side mounted slot-loading DVD Player. The DVD section not only plays DVDs, but can also play CDs, SVCDs, VCDs, MP3 and JPEG CDs.
In addition, the LED42C45RQD also provides additional AV inputs (HDMI, component, composite video), as well as a USB slot for accessing compatible content from flash drives or digital cameras. The set also has a digital optical audio output for connection to a home theater audio system.
The LED42C45RQD also has a built-in ATSC/QAM tuner for direct reception of the digital over-the-air and digital unscrambled cable channels. An added bonus is an included headphone jack. However, LED42C45RQD does not have internet streaming or 3D features and, of course, the built-in DVD player cannot play Blu-ray Discs. However, this TV combo may be just solution you are looking for.
For more suggestions, check out my current list of TV Combos.