If you’re determined to travel between the Yucatán, Veracruz and the US by the shortest route, avoiding Mexico City altogether, you’ll need to follow the coastal route. North of Tuxpán, there’s plenty of sandy beachfront, but access is difficult, beaches tend to be windswept and scrubby, and much of the area is marred by oil refineries. Several small-scale resorts have been developed here (such as La Pesca and the villages around Laguna Madre), but these tend to be popular with nearby city-dwellers and have little to offer compared with the beaches further south. It’s also very, very hot.
Another issue is drug violence – Tamaulipas, the focus of the bloody conflict between the Gulf Cartel and Los Zetas, had become the most dangerous part of Mexico by 2012, and though things have improved somewhat since then (the murder rate had halved by 2014), it remains blighted by shootings and kidnapping. If you have time you’d be well advised to cut inland from Tampico to Monterrey, where there’s plenty of metropolitan diversions and a larger choice of routes to the border.